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Goodwill and Intangible Assets - Changes in Goodwill (Details) - USD ($)
$ in Thousands
12 Months Ended
Sep. 30, 2019
Sep. 30, 2018
Sep. 30, 2017
Goodwill [Roll Forward]      
Goodwill, beginning $ 83,954 $ 58,517  
Goodwill attributable to acquisitions 84,330 25,437  
Goodwill, ending 168,284 83,954  
Merchant Services      
Goodwill [Roll Forward]      
Goodwill, beginning 69,666 49,173  
Goodwill attributable to acquisitions 38,806 20,493  
Goodwill, ending 108,472 69,666  
Accumulated impairment losses     $ 11,458
Proprietary Software and Payments      
Goodwill [Roll Forward]      
Goodwill, beginning 14,288 9,344  
Goodwill attributable to acquisitions 45,524 4,944  
Goodwill, ending 59,812 14,288  
Accumulated impairment losses     0
Other      
Goodwill [Roll Forward]      
Goodwill, beginning 0 0  
Goodwill attributable to acquisitions 0 0  
Goodwill, ending $ 0 $ 0  
Accumulated impairment losses     $ 0