Borrowings - Schedule of Debt Redemption (Details) - Senior Notes	12 Months Ended
Sep. 30, 2020
6 3/4% Senior Notes Maturing March of 2025
Debt Instrument, Redemption [Line Items]
Debt instrument stated interest rate (percent)	6.75%
Debt instrument, redemption price (percent)	106.75%
Percentage of principal amount redeemed	35.00%
Percentage of principal amount outstanding after redemption	65.00%
6 3/4% Senior Notes Maturing March of 2025 \| Debt Instrument, Redemption, Period One
Debt Instrument, Redemption [Line Items]
Debt instrument, redemption price (percent)	100.00%
6 3/4% Senior Notes Maturing March of 2025 \| Debt Instrument, Redemption, Period Two
Debt Instrument, Redemption [Line Items]
Debt instrument, redemption price (percent)	105.063%
6 3/4% Senior Notes Maturing March of 2025 \| Debt Instrument, Redemption, Period Three
Debt Instrument, Redemption [Line Items]
Debt instrument, redemption price (percent)	103.375%
6 3/4% Senior Notes Maturing March of 2025 \| Debt Instrument, Redemption, Period Four
Debt Instrument, Redemption [Line Items]
Debt instrument, redemption price (percent)	101.688%
6 3/4% Senior Notes Maturing March of 2025 \| Debt Instrument, Redemption, Period Five
Debt Instrument, Redemption [Line Items]
Debt instrument, redemption price (percent)	100.00%
5 7/8% Senior Notes Maturing October 2027
Debt Instrument, Redemption [Line Items]
Debt instrument stated interest rate (percent)	5.88%
Debt instrument, redemption price (percent)	105.875%
Percentage of principal amount redeemed	35.00%
Percentage of principal amount outstanding after redemption	65.00%
5 7/8% Senior Notes Maturing October 2027 \| Debt Instrument, Redemption, Period One
Debt Instrument, Redemption [Line Items]
Debt instrument, redemption price (percent)	100.00%
5 7/8% Senior Notes Maturing October 2027 \| Debt Instrument, Redemption, Period Two
Debt Instrument, Redemption [Line Items]
Debt instrument, redemption price (percent)	102.938%
5 7/8% Senior Notes Maturing October 2027 \| Debt Instrument, Redemption, Period Three
Debt Instrument, Redemption [Line Items]
Debt instrument, redemption price (percent)	101.958%
5 7/8% Senior Notes Maturing October 2027 \| Debt Instrument, Redemption, Period Four
Debt Instrument, Redemption [Line Items]
Debt instrument, redemption price (percent)	100.979%
5 7/8% Senior Notes Maturing October 2027 \| Debt Instrument, Redemption, Period Five
Debt Instrument, Redemption [Line Items]
Debt instrument, redemption price (percent)	100.00%
7 1/4% Senior Notes Maturing October 2029
Debt Instrument, Redemption [Line Items]
Debt instrument stated interest rate (percent)	7.25%
Debt instrument, redemption price (percent)	107.25%
Percentage of principal amount redeemed	35.00%
Percentage of principal amount outstanding after redemption	65.00%
7 1/4% Senior Notes Maturing October 2029 \| Debt Instrument, Redemption, Period One
Debt Instrument, Redemption [Line Items]
Debt instrument, redemption price (percent)	100.00%
7 1/4% Senior Notes Maturing October 2029 \| Debt Instrument, Redemption, Period Two
Debt Instrument, Redemption [Line Items]
Debt instrument, redemption price (percent)	103.625%
7 1/4% Senior Notes Maturing October 2029 \| Debt Instrument, Redemption, Period Three
Debt Instrument, Redemption [Line Items]
Debt instrument, redemption price (percent)	102.417%
7 1/4% Senior Notes Maturing October 2029 \| Debt Instrument, Redemption, Period Four
Debt Instrument, Redemption [Line Items]
Debt instrument, redemption price (percent)	101.208%
7 1/4% Senior Notes Maturing October 2029 \| Debt Instrument, Redemption, Period Five
Debt Instrument, Redemption [Line Items]
Debt instrument, redemption price (percent)	100.00%

Debt Instrument, Redemption Price, Percentage of Principal Amount Outstanding After Redemption

No definition available.

Name:	bzh_DebtInstrumentRedemptionPricePercentageofPrincipalAmountOutstandingAfterRedemption
Namespace Prefix:	bzh_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Contractual interest rate for funds borrowed, under the debt agreement.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.22(a)(1))
-URI http://asc.fasb.org/extlink&oid=6877327&loc=d3e13212-122682

+ Details

Name:	us-gaap_DebtInstrumentInterestRateStatedPercentage
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

Name:	us-gaap_DebtInstrumentRedemptionLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage price of original principal amount of debt at which debt can be redeemed by the issuer.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 470
-Section 50
-Paragraph 3
-Subparagraph e
-URI http://asc.fasb.org/extlink&oid=75038535&loc=d3e64711-112823

+ Details

Name:	us-gaap_DebtInstrumentRedemptionPricePercentage
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of principal amount of debt redeemed.

+ References

No definition available.

+ Details

Name:	us-gaap_DebtInstrumentRedemptionPricePercentageOfPrincipalAmountRedeemed
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	us-gaap_LongtermDebtTypeAxis=us-gaap_SeniorNotesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=bzh_A634SeniorNotesMaturingMarchof2025Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentRedemptionPeriodAxis=us-gaap_DebtInstrumentRedemptionPeriodOneMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentRedemptionPeriodAxis=us-gaap_DebtInstrumentRedemptionPeriodTwoMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentRedemptionPeriodAxis=us-gaap_DebtInstrumentRedemptionPeriodThreeMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentRedemptionPeriodAxis=us-gaap_DebtInstrumentRedemptionPeriodFourMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentRedemptionPeriodAxis=us-gaap_DebtInstrumentRedemptionPeriodFiveMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=bzh_A578SeniorNotesMaturingOctober2027Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=bzh_A714SeniorNotesMaturingOctober2029Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: