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- Narrative (Details) (USD $)
3 Months Ended 6 Months Ended
Mar. 31, 2015
Mar. 31, 2015
Mar. 31, 2014
Sep. 30, 2014
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Total stock-based compensation included in general and administrative expenses $ 1,500,000us-gaap_AllocatedShareBasedCompensationExpense $ 2,900,000us-gaap_AllocatedShareBasedCompensationExpense    
Total stock-based compensation included in general and administrative expenses, net of tax 1,100,000us-gaap_AllocatedShareBasedCompensationExpenseNetOfTax 2,200,000us-gaap_AllocatedShareBasedCompensationExpenseNetOfTax    
Number of shares surrendered by employees (shares)   9,899us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation 21,772us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation  
Payments Related to Tax Withholding for Share-based Compensation   185,000us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation 414,000us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation  
SSARs / Stock Options        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Intrinsic value of SSAR/stock options outstanding 1,400,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
1,400,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
   
SSARs/stock options weighted average expected life   2 years 3 months    
Aggregate intrinsic value of exercisable SSARs/stock options 1,200,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingAggregateIntrinsicValue
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
1,200,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingAggregateIntrinsicValue
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
   
Nonvested Stock Awards        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Unrecognized compensation costs related to non-vested stock awards $ 14,300,000us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions
/ us-gaap_AwardTypeAxis
= bzh_NonvestedStockAwardsMember
$ 14,300,000us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions
/ us-gaap_AwardTypeAxis
= bzh_NonvestedStockAwardsMember
  $ 10,000,000us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions
/ us-gaap_AwardTypeAxis
= bzh_NonvestedStockAwardsMember
Weighted average period to recognize remaining cost   2 years 10 months 12 days    
Performance Shares        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Number of shares of performance-based restricted stock issued (shares)   194,341us-gaap_StockIssuedDuringPeriodSharesNewIssues
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
   
Non-vested stock performance period (years)   3 years    
Award vesting period   3 years    
Granted   $ 19.90us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
   
Expected dividend yield on performance shares (percent)   0.00%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
   
Expected volatility rate range minimum (percent)   29.00%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRateMinimum
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
   
Expected volatility rate range maximum (percent)   185.80%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRateMaximum
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
   
Risk free interest rate   0.94%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
   
Minimum | Performance Shares        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting percent of target number   0.00%bzh_SharebasedCompensationArrangementbySharebasedPaymentAwardEquityInstrumentsOtherthanOptionsVestingPercentofTargetNumber
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
/ us-gaap_RangeAxis
= us-gaap_MinimumMember
   
Maximum | Performance Shares        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting percent of target number   150.00%bzh_SharebasedCompensationArrangementbySharebasedPaymentAwardEquityInstrumentsOtherthanOptionsVestingPercentofTargetNumber
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
/ us-gaap_RangeAxis
= us-gaap_MaximumMember
   
Pre-tax Income Performance Shares | Minimum | Performance Shares        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Equity instruments other than options, payout percent   50.00%bzh_SharebasedCompensationArrangementbySharebasedPaymentAwardEquityInstrumentsOtherthanOptionsPayoutPercent
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
/ us-gaap_PlanNameAxis
= bzh_PretaxIncomePerformanceSharesMember
/ us-gaap_RangeAxis
= us-gaap_MinimumMember
   
Pre-tax Income Performance Shares | Maximum | Performance Shares        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Equity instruments other than options, payout percent   200.00%bzh_SharebasedCompensationArrangementbySharebasedPaymentAwardEquityInstrumentsOtherthanOptionsPayoutPercent
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
/ us-gaap_PlanNameAxis
= bzh_PretaxIncomePerformanceSharesMember
/ us-gaap_RangeAxis
= us-gaap_MaximumMember