Intangible Assets - Schedule of Finite-Lived Intangible Assets (Details) - USD ($) $ in Millions	Sep. 30, 2023	Sep. 30, 2022
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	$ 175.4	$ 170.9
Accumulated amortization	(72.8)	(56.0)
Net carrying amount	102.6	114.9
Trademarks and trade names
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	29.6	29.6
Accumulated amortization	(10.5)	(9.2)
Net carrying amount	19.1	20.4
Reacquired franchise rights
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	122.1	118.0
Accumulated amortization	(49.4)	(36.5)
Net carrying amount	72.7	81.5
Customer relationships
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	16.8	16.6
Accumulated amortization	(8.3)	(6.9)
Net carrying amount	8.5	9.7
Other intangible assets
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	6.9	6.7
Accumulated amortization	(4.6)	(3.4)
Net carrying amount	$ 2.3	$ 3.3