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Acquisitions and Divestitures - Additional Information (Detail) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
Jun. 30, 2021
Jun. 30, 2021
Jun. 30, 2020
Acquisitions And Divestitures [Line Items]      
Cash paid for business acquisition   $ 707 $ 59
Goodwill, Acquired During Period   273  
Business divestitures, net of cash divested   19 0
Goodwill, Written off Related to Sale of Business Unit   7  
Building Solutions EMEA/LA      
Acquisitions And Divestitures [Line Items]      
Goodwill, Acquired During Period   21  
Goodwill, Written off Related to Sale of Business Unit   0  
Building Solutions Asia Pacific      
Acquisitions And Divestitures [Line Items]      
Goodwill, Acquired During Period   0  
Goodwill, Written off Related to Sale of Business Unit   7  
Global Products      
Acquisitions And Divestitures [Line Items]      
Goodwill, Acquired During Period   235  
Goodwill, Written off Related to Sale of Business Unit   0  
Building Solutions North America      
Acquisitions And Divestitures [Line Items]      
Goodwill, Acquired During Period   17  
Goodwill, Written off Related to Sale of Business Unit   0  
Business Divestitures, Not Specific | Building Solutions Asia Pacific      
Acquisitions And Divestitures [Line Items]      
Proceeds from Divestiture of Businesses $ 27 27  
Business divestitures, net of cash divested   19  
Goodwill, Written off Related to Sale of Business Unit   7  
Silent-Aire      
Acquisitions And Divestitures [Line Items]      
Purchase price, net of cash acquired 751    
Cash paid for business acquisition 661    
Business Combination, Contingent Consideration, Liability 90 90  
Business Combination, Contingent Consideration Arrangements, Range of Outcomes, Value, High 250 250  
Silent-Aire | Global Products      
Acquisitions And Divestitures [Line Items]      
Goodwill, Acquired During Period $ 235    
Individually Immaterial Acquisitions      
Acquisitions And Divestitures [Line Items]      
Purchase price, net of cash acquired   58 63
Cash paid for business acquisition   46 59
Individually Immaterial Acquisitions | Building Solutions EMEA/LA      
Acquisitions And Divestitures [Line Items]      
Goodwill, Acquired During Period   21 23
Individually Immaterial Acquisitions | Global Products      
Acquisitions And Divestitures [Line Items]      
Goodwill, Acquired During Period     $ 19
Individually Immaterial Acquisitions | Building Solutions North America      
Acquisitions And Divestitures [Line Items]      
Goodwill, Acquired During Period   $ 17