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Stockholders' Equity - Additional Information (Detail) (USD $)
0 Months Ended 3 Months Ended 12 Months Ended 1 Months Ended 7 Months Ended 0 Months Ended 9 Months Ended
Jul. 02, 2014
Dec. 31, 2014
Sep. 30, 2014
Jun. 30, 2014
Mar. 31, 2014
Sep. 30, 2013
Mar. 31, 2013
Subsidiary
Dec. 31, 2014
Dec. 31, 2013
Dec. 31, 2012
Aug. 31, 2013
Jul. 31, 2013
Sep. 30, 2014
Sep. 29, 2014
Sep. 30, 2014
Jul. 30, 2014
Jun. 28, 2013
Aug. 02, 2013
Jan. 31, 2008
Class of Stock [Line Items]                                      
Preferred dividends description               Our 4.0% Series A Convertible Preferred Stock ceased accruing daily dividends as a result of redemption in August 2013. Our 4.0% Series B Convertible Preferred Stock ceased accruing daily dividends as a result of the conversion of all of the remaining outstanding shares on September 30, 2014.                      
Preferred shares outstanding   0us-gaap_PreferredStockSharesOutstanding           0us-gaap_PreferredStockSharesOutstanding                      
Preferred dividends accrued                   $ 4,000,000us-gaap_DividendsPayableCurrent                    
Payment for preferred stock redemption                  474,000,000us-gaap_PaymentsForRepurchaseOfPreferredStockAndPreferenceStock                     
Preferred stock redemption premium           232,000,000us-gaap_PreferredStockRedemptionPremium      232,000,000us-gaap_PreferredStockRedemptionPremium                     
Terms of conversion - closing price of common stock $ 22.24dan_TermsOfConversionClosingStockPrice                                    
Terms of conversion - consecutive trading days 20 days                                    
Common stock conversion price of preferred shares $ 11.93dan_StockConversionPricePerShare                                    
Conversion Notice Period 90 days                                    
Common stock, shares authorized   450,000,000us-gaap_CommonStockSharesAuthorized           450,000,000us-gaap_CommonStockSharesAuthorized 450,000,000us-gaap_CommonStockSharesAuthorized                    
Common stock, par value   $ 0.01us-gaap_CommonStockParOrStatedValuePerShare           $ 0.01us-gaap_CommonStockParOrStatedValuePerShare $ 0.01us-gaap_CommonStockParOrStatedValuePerShare                    
Common stock, shares issued   167,659,047us-gaap_CommonStockSharesIssued           167,659,047us-gaap_CommonStockSharesIssued                      
Common stock, shares outstanding   166,070,057us-gaap_CommonStockSharesOutstanding           166,070,057us-gaap_CommonStockSharesOutstanding 145,338,342us-gaap_CommonStockSharesOutstanding                    
Treasury stock, shares   1,588,990us-gaap_TreasuryStockShares           1,588,990us-gaap_TreasuryStockShares 18,742,288us-gaap_TreasuryStockShares                    
Quarterly dividend declared   $ 0.05us-gaap_CommonStockDividendsPerShareDeclared $ 0.05us-gaap_CommonStockDividendsPerShareDeclared $ 0.05us-gaap_CommonStockDividendsPerShareDeclared $ 0.05us-gaap_CommonStockDividendsPerShareDeclared     $ 0.20us-gaap_CommonStockDividendsPerShareDeclared $ 0.20us-gaap_CommonStockDividendsPerShareDeclared $ 0.20us-gaap_CommonStockDividendsPerShareDeclared                  
Dividends declared and paid               32,000,000dan_DividendsDeclaredAndPaidCommonStockCash                      
Treasury stock reissued               14,879,935us-gaap_StockIssuedDuringPeriodSharesTreasuryStockReissued                      
Treasury stock reissued, charge to additional paid-in capital               127,000,000dan_TreasuryStockReissuedAtLowerThanRepurchasePriceOther                      
Treasury shares retired               14,600,000us-gaap_TreasuryStockSharesRetired                      
Treasury stock retired, charge to additional paid-in capital               0us-gaap_TreasuryStockRetiredCostMethodAmount                      
Share repurchase program amount                               1,400,000,000us-gaap_StockRepurchaseProgramAuthorizedAmount1 1,000,000,000us-gaap_StockRepurchaseProgramAuthorizedAmount1    
Cash spent to repurchase common stock               260,000,000us-gaap_PaymentsForRepurchaseOfCommonStock 337,000,000us-gaap_PaymentsForRepurchaseOfCommonStock 15,000,000us-gaap_PaymentsForRepurchaseOfCommonStock                  
Shares repurchased               12,215,451us-gaap_TreasuryStockSharesAcquired                      
Available for future share repurchases   311,000,000us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1           311,000,000us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1                      
Number of subsidiaries in which noncontrolling interests were purchased             3dan_NumberOfSubsidiariesInWhichNoncontrollingInterestsWerePurchased                        
Payments to Noncontrolling Interests             7,000,000us-gaap_PaymentsToMinorityShareholders    7,000,000us-gaap_PaymentsToMinorityShareholders                     
Series A Preferred Stock [Member]                                      
Class of Stock [Line Items]                                      
Preferred shares issued                                     2,500,000.0us-gaap_PreferredStockSharesIssued
/ us-gaap_StatementClassOfStockAxis
= us-gaap_SeriesAPreferredStockMember
Series A and Series B preferred stock dividend rate percentage                       4.00%us-gaap_PreferredStockDividendRatePercentage
/ us-gaap_StatementClassOfStockAxis
= us-gaap_SeriesAPreferredStockMember
             
Preferred shares outstanding   0us-gaap_PreferredStockSharesOutstanding
/ us-gaap_StatementClassOfStockAxis
= us-gaap_SeriesAPreferredStockMember
          0us-gaap_PreferredStockSharesOutstanding
/ us-gaap_StatementClassOfStockAxis
= us-gaap_SeriesAPreferredStockMember
0us-gaap_PreferredStockSharesOutstanding
/ us-gaap_StatementClassOfStockAxis
= us-gaap_SeriesAPreferredStockMember
                   
Payment for preferred stock redemption                     474,000,000us-gaap_PaymentsForRepurchaseOfPreferredStockAndPreferenceStock
/ us-gaap_StatementClassOfStockAxis
= us-gaap_SeriesAPreferredStockMember
               
Payment of preferred stock redemption costs                     3,000,000dan_PaymentOfPreferredStockRedemptionCosts
/ us-gaap_StatementClassOfStockAxis
= us-gaap_SeriesAPreferredStockMember
               
Preferred stock carrying value                                   242,000,000us-gaap_PreferredStockValue
/ us-gaap_StatementClassOfStockAxis
= us-gaap_SeriesAPreferredStockMember
 
Preferred stock redemption premium                     232,000,000us-gaap_PreferredStockRedemptionPremium
/ us-gaap_StatementClassOfStockAxis
= us-gaap_SeriesAPreferredStockMember
               
Preferred Stock [Member]                                      
Class of Stock [Line Items]                                      
Preferred dividends accrued                 4,000,000us-gaap_DividendsPayableCurrent
/ us-gaap_StatementClassOfStockAxis
= us-gaap_PreferredStockMember
                   
Series B Preferred Stock [Member]                                      
Class of Stock [Line Items]                                      
Preferred shares issued                                     5,400,000.0us-gaap_PreferredStockSharesIssued
/ us-gaap_StatementClassOfStockAxis
= us-gaap_SeriesBPreferredStockMember
Series A and Series B preferred stock dividend rate percentage                             4.00%us-gaap_PreferredStockDividendRatePercentage
/ us-gaap_StatementClassOfStockAxis
= us-gaap_SeriesBPreferredStockMember
       
Preferred shares outstanding   0us-gaap_PreferredStockSharesOutstanding
/ us-gaap_StatementClassOfStockAxis
= us-gaap_SeriesBPreferredStockMember
          0us-gaap_PreferredStockSharesOutstanding
/ us-gaap_StatementClassOfStockAxis
= us-gaap_SeriesBPreferredStockMember
3,803,774us-gaap_PreferredStockSharesOutstanding
/ us-gaap_StatementClassOfStockAxis
= us-gaap_SeriesBPreferredStockMember
                   
Shares of preferred stock converted               1,772,693us-gaap_ConversionOfStockSharesConverted1
/ us-gaap_StatementClassOfStockAxis
= us-gaap_SeriesBPreferredStockMember
1,417,425us-gaap_ConversionOfStockSharesConverted1
/ us-gaap_StatementClassOfStockAxis
= us-gaap_SeriesBPreferredStockMember
      1,506,972us-gaap_ConversionOfStockSharesConverted1
/ us-gaap_StatementClassOfStockAxis
= us-gaap_SeriesBPreferredStockMember
2,296,802us-gaap_ConversionOfStockSharesConverted1
/ us-gaap_StatementClassOfStockAxis
= us-gaap_SeriesBPreferredStockMember
         
Common shares issued upon conversion                 11,985,254us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities
/ us-gaap_StatementClassOfStockAxis
= us-gaap_SeriesBPreferredStockMember
      12,631,780us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities
/ us-gaap_StatementClassOfStockAxis
= us-gaap_SeriesBPreferredStockMember
19,517,593us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities
/ us-gaap_StatementClassOfStockAxis
= us-gaap_SeriesBPreferredStockMember
         
Total fair value of the conversions                 249,000,000dan_SharesSubjectToConversionFairValueOfConversions
/ us-gaap_StatementClassOfStockAxis
= us-gaap_SeriesBPreferredStockMember
      250,000,000dan_SharesSubjectToConversionFairValueOfConversions
/ us-gaap_StatementClassOfStockAxis
= us-gaap_SeriesBPreferredStockMember
409,000,000dan_SharesSubjectToConversionFairValueOfConversions
/ us-gaap_StatementClassOfStockAxis
= us-gaap_SeriesBPreferredStockMember
         
Additional Paid-in Capital [Member]                                      
Class of Stock [Line Items]                                      
Treasury stock retired, charge to additional paid-in capital               $ (294,000,000)us-gaap_TreasuryStockRetiredCostMethodAmount
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_AdditionalPaidInCapitalMember