Debt - Total Debt (Details) - USD ($) $ in Thousands	12 Months Ended
Sep. 30, 2021	Sep. 30, 2020
Debt Instrument [Line Items]
Less: Unamortized debt issuance costs	$ (12,031)	$ (14,949)
Total debt	916,344	921,414
Less: Current maturities and short-term debt	(13,313)	(10,650)
Long-term debt, net of current portion	$ 903,031	910,764
Credit Agreement \| Senior Secured Term Loan Facility \| LIBOR
Debt Instrument [Line Items]
Basis spread on variable rate	2.00%
Senior Secured Term Loan Facility
Debt Instrument [Line Items]
Long-term debt	$ 928,375	$ 936,363

Amount of short-term debt and current maturity of long-term debt and capital lease obligations due within one year or the normal operating cycle, if longer.

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Percentage points added to the reference rate to compute the variable rate on the debt instrument.

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Amount, before unamortized (discount) premium and debt issuance costs, of long-term debt. Includes, but is not limited to, notes payable, bonds payable, commercial loans, mortgage loans, convertible debt, subordinated debt and other types of debt.

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Amount of unamortized debt discount (premium) and debt issuance costs.

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Amount, after unamortized (discount) premium and debt issuance costs, of long-term debt. Includes, but not limited to, notes payable, bonds payable, debentures, mortgage loans and commercial paper. Excludes capital lease obligations.

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Amount after unamortized (discount) premium and debt issuance costs of long-term debt classified as noncurrent and excluding amounts to be repaid within one year or the normal operating cycle, if longer. Includes, but not limited to, notes payable, bonds payable, debentures, mortgage loans and commercial paper. Excludes capital lease obligations.

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