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Intangible Assets - Schedule of Finite-Lived Intangible Assets (Details) - USD ($)
$ in Millions
Sep. 30, 2025
Sep. 30, 2024
Finite-Lived Intangible Assets [Line Items]    
Gross carrying amount $ 173.9 $ 173.5
Accumulated amortization (91.4) (83.2)
Net carrying amount 82.5 90.3
Trademarks and trade names    
Finite-Lived Intangible Assets [Line Items]    
Gross carrying amount 29.5 29.2
Accumulated amortization (12.7) (11.4)
Net carrying amount 16.8 17.8
Reacquired franchise rights    
Finite-Lived Intangible Assets [Line Items]    
Gross carrying amount 122.3 122.2
Accumulated amortization (63.9) (58.7)
Net carrying amount 58.4 63.5
Customer relationships    
Finite-Lived Intangible Assets [Line Items]    
Gross carrying amount 14.7 15.1
Accumulated amortization (8.5) (7.9)
Net carrying amount 6.2 7.2
Other intangible assets    
Finite-Lived Intangible Assets [Line Items]    
Gross carrying amount 7.4 7.0
Accumulated amortization (6.3) (5.2)
Net carrying amount $ 1.1 $ 1.8