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v3.22.2.2

Description of Business (Details) | Sep. 30, 2022 state region
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Description of Business [Abstract] |
Number of states in which home building segments operate | state | 13
Number of regions in which entity operates | region | 3

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- Definition Description of Business [Abstract] + References No definition available. + Details
Name: | bzh_DescriptionofBusinessAbstract
Namespace Prefix: | bzh_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

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- Definition Number of Regions in which Entity Operates + References No definition available. + Details
Name: | bzh_NumberofRegionsinwhichEntityOperates
Namespace Prefix: | bzh_
Data Type: | xbrli:integerItemType
Balance Type: | na
Period Type: | instant

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- Definition The number of states the entity operates in as of the balance sheet date. + References No definition available. + Details
Name: | us-gaap_NumberOfStatesInWhichEntityOperates
Namespace Prefix: | us-gaap_
Data Type: | xbrli:integerItemType
Balance Type: | na
Period Type: | instant