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Intangible Assets, Goodwill and Acquisitions - Summary of Goodwill (Details) - USD ($)
$ in Millions
9 Months Ended 12 Months Ended
Jun. 30, 2022
Sep. 30, 2021
Goodwill [Line Items]    
Beginning balance $ 1,950.8 $ 1,859.3
Acquisitions 54.6 [1] 91.5
Ending balance 2,005.4 1,950.8
Maintenance Services    
Goodwill [Line Items]    
Beginning balance 1,758.0 1,680.4
Acquisitions 31.4 [1] 77.6
Ending balance 1,789.4 1,758.0
Development Services    
Goodwill [Line Items]    
Beginning balance 192.8 178.9
Acquisitions 23.2 [1] 13.9
Ending balance $ 216.0 $ 192.8
[1] The acquisitions adjustment includes the immaterial impact of foreign currency adjustments during the period