Long-Term Debt - Additional Information (Details) - USD ($) $ in Millions						12 Months Ended
		Aug. 31, 2023	Aug. 28, 2023	Apr. 22, 2022	Dec. 18, 2013	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021	Jun. 22, 2022
Debt Instrument [Line Items]
Debt repayments						$ 459.0	$ 1,006.3	$ 10.4
Loss on debt extinguishment	[1]					8.3	12.6	0.0
Debt voluntary repayment						554.5	374.4	24.6
Debt borrowings during the period						549.5	391.7	$ 34.5
Long-term debt, fair value						$ 900.1	$ 1,317.1
Receivables Financing Agreement | Wholly-owned Subsidiary
Debt Instrument [Line Items]
Credit agreement, maximum borrowing capacity									$ 275.0
Interest period term						6 months
Weighted average interest rate						6.30%	2.40%
Commitment fee for unused balance of facility						0.40%
Debt voluntary repayment						$ 549.5	$ 392.0
Debt borrowings during the period						$ 554.5	374.4
SOFR | Maximum | Receivables Financing Agreement | Wholly-owned Subsidiary
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate						170.00%
SOFR | Minimum | Receivables Financing Agreement | Wholly-owned Subsidiary
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate						140.00%
Series B Term Loan | SOFR
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate				0.50%
Series B Term Loan | ABR
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate				1.50%
Credit Agreement | First Lien Credit Facility Term Loans
Debt Instrument [Line Items]
Credit agreement date					Dec. 18, 2013
Debt instrument, term					7 years
Credit agreement, maximum borrowing capacity					$ 1,460.0
Credit Agreement | First Lien Revolving Credit Facility
Debt Instrument [Line Items]
Debt instrument, term					5 years
Credit agreement, maximum borrowing capacity					$ 210.0
Amended Credit Agreement
Debt Instrument [Line Items]
Loss on debt extinguishment			$ (8.3)	$ (12.6)
Percentage of prepayment premium		1.00%
Percentage of principle balance used to calculate debt repayments amount of quarterly installments due						0.25%
Debt borrowings during the period			$ 450.0
Amended Credit Agreement | First Lien Revolving Credit Facility
Debt Instrument [Line Items]
Debt instrument, term				5 years
Credit agreement, maximum borrowing capacity				$ 300.0
Amended Credit Agreement | Series B Term Loan
Debt Instrument [Line Items]
Debt instrument, term				7 years
Credit agreement, maximum borrowing capacity				$ 1,200.0
Debt instrument, original discount				$ 12.0
Debt repayments						$ 459.0	$ 1,006.3
Debt instrument, maturity date				Apr. 22, 2029
Debt instrument, effective interest rate				3.42%
Weighted average interest rate						7.82%	3.76%
Previous Revolving Credit Facility | First Lien Revolving Credit Facility
Debt Instrument [Line Items]
Credit agreement, maximum borrowing capacity				$ 260.0
Line of credit facility, amount outstanding balance						$ 0.0	$ 0.0
Letters of credits, outstanding amount						$ 42.6	49.1
Previous Revolving Credit Facility | First Lien Revolving Credit Facility | Scenario One Depending on Leverage Ratio
Debt Instrument [Line Items]
Commitment fee for unused balance of facility						0.25%
Previous Revolving Credit Facility | First Lien Revolving Credit Facility | Scenario Two Depending on Leverage Ratio
Debt Instrument [Line Items]
Commitment fee for unused balance of facility						0.38%
Revolving Credit Facility | SOFR
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate				0.00%
Revolving Credit Facility | ABR
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate				1.00%
Revolving Credit Facility | ABR | Maximum
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate				1.50%
Revolving Credit Facility | ABR | Minimum
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate				1.00%
Revolving Credit Facility | First Lien Revolving Credit Facility
Debt Instrument [Line Items]
Debt instrument, term				5 years
Credit agreement, maximum borrowing capacity				$ 300.0
Debt repayments						$ 33.5	$ 165.0
Debt instrument, maturity date				Apr. 22, 2027
Weighted average interest rate						6.90%	2.30%
Debt borrowings during the period						$ 33.5	$ 165.0
Revolving Credit Facility | First Lien Revolving Credit Facility | LIBOR | Maximum
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate				2.50%
Revolving Credit Facility | First Lien Revolving Credit Facility | LIBOR | Minimum
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate				2.00%
Revolving Credit Facility | Series B Term Loan | SOFR | Maximum
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate				3.25%
Revolving Credit Facility | Series B Term Loan | SOFR | Minimum
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate				3.00%
Revolving Credit Facility | Series B Term Loan | ABR | Maximum
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate				2.25%
Revolving Credit Facility | Series B Term Loan | ABR | Minimum
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate				2.00%

[1] Represents losses on the extinguishment of debt related to Amendments No. 6 and No. 7 to the Credit Agreement, in the fiscal years ended September 30, 2022 and 2023, respectively, and includes accelerated amortization of deferred financing fees and original issue discount as well as fees paid to lenders and third parties.