Operating Segments and Geographic Information - Reconciliation of Total Reportable Segments' Revenues and EBITDA to Consolidated Revenues and Consolidated Income Before Taxes (Details) - USD ($) $ in Thousands	3 Months Ended								12 Months Ended
	Dec. 31, 2019	Sep. 29, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018	Sep. 30, 2018	Jul. 01, 2018	Apr. 01, 2018	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Total Segment Revenues	$ 549,688	$ 533,098	$ 548,352	$ 500,140	$ 552,052	$ 554,037	$ 560,898	$ 498,715	$ 2,131,278	$ 2,165,702	$ 2,087,185
Amortization of intangibles									(74,609)	(75,140)	(90,188)
Depreciation expense									(40,400)	(38,300)	(38,600)
Severance, restructuring, and acquisition integration costs	(21,000)	(3,000)	(2,500)	(0)	(2,200)	(4,600)	(4,600)	(11,200)	(26,544)	(22,625)	(41,893)
Gain from patent litigation									0	(62,141)	0
Operating income	$ 43,400	$ 57,542	$ 58,775	$ 47,490	$ 71,264	$ 129,160	$ 68,706	$ 44,878	207,207	314,008	233,641
Interest expense, net									(55,814)	(60,839)	(82,651)
Non-operating pension benefit (cost)									1,017	(99)	(561)
Loss on debt extinguishment									0	(22,990)	(52,441)
Consolidated income from continuing operations before taxes									152,410	230,080	97,988
Reportable Segment
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Total Segment Revenues									2,131,278	2,165,702	2,087,185
Deferred revenue adjustments									0	0	0
Total Segment EBITDA									351,223	394,656	405,429
Amortization of intangibles									(74,609)	(75,140)	(90,188)
Depreciation expense									(40,409)	(38,309)	(38,624)
Severance, restructuring, and acquisition integration costs									(26,544)	(22,625)	(41,893)
Purchase accounting effects related to acquisitions									592	1,690	6,133
Amortization of software development intangible assets									(525)	(79)	0
Loss on sale of assets (3)									0	94	1,013
Costs related to patent litigation									0	(2,634)	0
Gain from patent litigation									0	(62,141)	0
Income from equity method investment									0	0	7,502
Operating income									207,207	314,008	233,641
Interest expense, net									(55,814)	(60,839)	(82,651)
Eliminations
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Operating income									(1,337)	(2,218)	(1,439)
Enterprise Solutions
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Total Segment Revenues									1,081,232	1,095,900	1,054,847
Severance, restructuring, and acquisition integration costs									(11,050)	(14,862)	(28,146)
Enterprise Solutions | Reportable Segment
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Total Segment EBITDA									162,276	190,910	196,554
Amortization of intangibles									(23,500)	(22,255)	(37,245)
Depreciation expense									(20,765)	(19,374)	(19,255)
Severance, restructuring, and acquisition integration costs									(11,050)	(14,863)	(28,146)
Purchase accounting effects related to acquisitions									592	1,690	6,133
Segment revenues | Reportable Segment
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Total Segment Revenues									2,131,278	2,165,702	2,087,185
Segment revenues | Enterprise Solutions | Reportable Segment
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Total Segment Revenues									$ 1,081,232	$ 1,095,900	$ 1,054,847