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Stock-based Compensation - Nonvested Stock Awards (Details) (Nonvested Stock Awards and Performance Shares, USD $)
3 Months Ended 6 Months Ended
Mar. 31, 2015
Mar. 31, 2015
Nonvested Stock Awards and Performance Shares
   
Shares    
Beginning of period 968,439us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= bzh_NonvestedStockAwardsAndPerformanceSharesMember
746,567us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= bzh_NonvestedStockAwardsAndPerformanceSharesMember
Granted 0us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= bzh_NonvestedStockAwardsAndPerformanceSharesMember
390,870us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= bzh_NonvestedStockAwardsAndPerformanceSharesMember
Vested 271us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod
/ us-gaap_AwardTypeAxis
= bzh_NonvestedStockAwardsAndPerformanceSharesMember
63,078us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod
/ us-gaap_AwardTypeAxis
= bzh_NonvestedStockAwardsAndPerformanceSharesMember
Forfeited 14,560us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod
/ us-gaap_AwardTypeAxis
= bzh_NonvestedStockAwardsAndPerformanceSharesMember
120,751us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod
/ us-gaap_AwardTypeAxis
= bzh_NonvestedStockAwardsAndPerformanceSharesMember
End of period 953,608us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= bzh_NonvestedStockAwardsAndPerformanceSharesMember
953,608us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= bzh_NonvestedStockAwardsAndPerformanceSharesMember
Weighted Average Grant Date Fair Value    
Beginning of period $ 18.31us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= bzh_NonvestedStockAwardsAndPerformanceSharesMember
$ 15.76us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= bzh_NonvestedStockAwardsAndPerformanceSharesMember
Granted $ 0.00us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= bzh_NonvestedStockAwardsAndPerformanceSharesMember
$ 19.07us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= bzh_NonvestedStockAwardsAndPerformanceSharesMember
Vested $ 18.85us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= bzh_NonvestedStockAwardsAndPerformanceSharesMember
$ 15.90us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= bzh_NonvestedStockAwardsAndPerformanceSharesMember
Forfeited $ 19.11us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= bzh_NonvestedStockAwardsAndPerformanceSharesMember
$ 6.39us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= bzh_NonvestedStockAwardsAndPerformanceSharesMember
End of period $ 18.29us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= bzh_NonvestedStockAwardsAndPerformanceSharesMember
$ 18.29us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= bzh_NonvestedStockAwardsAndPerformanceSharesMember