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Identifiable Intangible Assets Schedule of Intangible Assets and Goodwill (Details) - USD ($)
 12 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2020
Indefinite-lived intangible assets:      
Goodwill $ 98,600,000 $ 115,100,000 $ 99,800,000
Intangible Assets, Gross, (Including Goodwill) 764,200,000 770,300,000  
Accumulated amortization:      
Intangible Assets, Net (Excluding Goodwill) 361,200,000 392,500,000  
Goodwill, Acquired During Period 12    
Indefinite-lived Intangible Assets, Foreign Currency Translation Gain (Loss) (9,700,000) 3,200,000  
i2O      
Accumulated amortization:      
Goodwill, Acquired During Period   12,100,000  
Business Combination-Related Identifiable Intangible [Member]      
Accumulated amortization:      
Accumulated Amortization 411,700,000 387,800,000  
Net book value 352,500,000 382,500,000  
Trademarks and Trade Names [Member]      
Indefinite-lived intangible assets:      
Trade names and trademarks 272,700,000 273,800,000  
Software and Software Development Costs [Member]      
Capitalized external-use software:      
Capitalized Computer Software, Gross 35,500,000 34,100,000  
Accumulated amortization 26,800,000 24,100,000  
Net book value 8,700,000 10,000,000.0  
Technology-Based Intangible Assets [Member]      
Finite-lived intangible assets:      
Technology 119,900,000 123,500,000  
Accumulated amortization:      
Accumulated Amortization 89,500,000 85,800,000  
Customer Relationships [Member]      
Finite-lived intangible assets:      
Customer relationships and other 371,600,000 373,000,000.0  
Accumulated amortization:      
Accumulated Amortization $ 322,200,000 $ 302,000,000.0