Condensed Consolidated Statements of Comprehensive Income (Loss) - USD ($) shares in Millions, $ in Millions	3 Months Ended
	Mar. 31, 2021	Mar. 31, 2020
Revenues:
Total revenues	$ 1,233.4	$ 1,173.6
Cost of revenues:
Total cost of revenues	674.3	665.6
Gross profit	559.1	508.0
Operating expenses:
Selling and marketing	92.0	91.4
Research and development	107.9	104.9
General and administrative	90.1	92.9
Total operating expenses	290.0	289.2
Operating income	269.1	218.8
Interest expense, net	(51.4)	(77.4)
Other income (expense), net	18.0	(15.3)
Equity in earnings of unconsolidated affiliates, net	0.3	0.7
Loss on extinguishment of debt	(0.3)	(2.8)
Income before income taxes	235.7	124.0
Provision for income taxes	60.8	24.8
Net income	$ 174.9	$ 99.2
Basic earnings per share	$ 0.68	$ 0.39
Diluted earnings per share	$ 0.65	$ 0.37
Basic weighted-average number of common shares outstanding	257.0	255.3
Diluted weighted-average number of common and common equivalent shares outstanding	268.1	265.6
Net income	$ 174.9	$ 99.2
Other comprehensive income (loss), net of tax:
Change in unrealized gain (loss) on interest rate swaps	0.5	(2.4)
Foreign currency exchange translation adjustment	8.4	(150.7)
Total other comprehensive income (loss), net of tax	8.9	(153.1)
Comprehensive income (loss)	183.8	(53.9)
Software-enabled Services [Member]
Revenues:
Total revenues	1,043.4	989.5
Cost of revenues:
Total cost of revenues	595.5	583.5
License, Maintenance and Related [Member]
Revenues:
Total revenues	190.0	184.1
Cost of revenues:
Total cost of revenues	$ 78.8	$ 82.1