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Stock-based Compensation - Stock options and SSARs outstanding (Details) (SSARs / Stock Options, USD $)
3 Months Ended 6 Months Ended
Mar. 31, 2015
Mar. 31, 2015
Dec. 31, 2014
Sep. 30, 2014
SSARs / Stock Options
       
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Shares outstanding at beginning of period (shares) 646,630us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
646,630us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
650,223us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
650,233us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
Options Granted 0us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
0us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
   
Share-Based Compensation Arrangement By ShareBased Payment Award, Exercises In Period 456us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
456us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
   
Share-based Compensation Arrangement by Share-based Payment Award, Expirations in Period 0bzh_ShareBasedCompensationArrangementByShareBasedPaymentAwardExpirationsInPeriod
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
0bzh_ShareBasedCompensationArrangementByShareBasedPaymentAwardExpirationsInPeriod
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
   
Share-based Compensation Arrangement by Share-based Payment Award, Forfeitures in Period 3,137us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
3,147us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
   
Exercisable at end of period (shares) 491,932us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
491,932us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
   
Vested or expected to vest in the future (shares) 646,437us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
646,437us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
   
Weighted average exercise price of shares outstanding at beginning of period (in US$ per share) $ 18.12us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
$ 18.12us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
$ 18.12us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
$ 18.12us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
Share-based Compensation Arrangements by Share-based Payment Award, Grants in Period, Weighted Average Exercise Price $ 0.00us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
$ 0.00us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
   
Share-based Compensation Arrangements by Share-based Payment Award, Exercises in Period, Weighted Average Exercise Price $ 12.07us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
$ 12.07us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
   
Share-based Compensation Arrangements by Share-based Payment Award, Expirations in Period, Weighted Average Exercise Price $ 0.00bzh_ShareBasedCompensationArrangementsByShareBasedPaymentAwardExpirationsInPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
$ 0.00bzh_ShareBasedCompensationArrangementsByShareBasedPaymentAwardExpirationsInPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
   
Share-based Compensation Arrangements by Share-based Payment Award, Forfeitures in Period, Weighted Average Exercise Price $ 20.32us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
$ 20.32us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
   
Weighted average exercise price of shares exercisable at end of period (in US$ per share) $ 18.39us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
$ 18.39us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
   
Weighted average exercise price of shares vested or expected to vest in the future (in US$ per share) $ 18.12us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember
$ 18.12us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= bzh_SsarsStockOptionsMember