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Significant Accounting Policies - Additional Information (Detail)
 12 Months Ended
Sep. 30, 2023
USD ($)
Segment
Sep. 30, 2022
USD ($)
Sep. 30, 2021
USD ($)
Accounting Policies [Abstract]      
Goodwill and other intangible assets increased from acquisitions $ 353,100,000 $ 45,300,000  
Business acquisition, goodwill for tax purposes 216,000,000.0 10,500,000  
Impairment charges 0    
Contract assets recorded in prepaid expenses and other current assets $ 5,300,000 5,900,000  
Revenue remaining obligation description As a practical expedient, because repair and maintenance service contracts have an original duration of one year or less, we do not consider the time value of money, and we do not disclose estimated revenue expected to be recognized in the future for performance obligations that are unsatisfied (or partially unsatisfied) at the end of the reporting period or when we expect to recognize such revenue.    
Contract liabilities recognized in revenue   126,100,000 $ 94,900,000
Reclassified out of accumulated other comprehensive income $ 0    
Total advertising and promotional expenses $ 36,000,000 $ 25,800,000 $ 14,800,000
Number of reporting segment | Segment 2