Income Taxes (Narrative) (Details) € in Thousands, $ in Thousands	1 Months Ended	12 Months Ended			36 Months Ended
	Mar. 30, 2019 EUR (€)	Dec. 31, 2019 USD ($)	Dec. 31, 2018 USD ($)	Dec. 31, 2017 USD ($)	Dec. 31, 2014 EUR (€)
Income Taxes [Line Items]
Percentage of earnings from continuing operations before income taxes attributable to the United States		22.00%
Deferred tax asset resulting from restructuring		$ 775,064	$ 759,143
Deferred tax benefit related to tax basis of intangible assets		107,842	(88,456)	$ 75,591
Valuation allowance against deferred tax asset		232,196	347,786
Increase (decrease) in the valuation allowance		(115,590)	(15,177)
Net operating loss carryforwards and tax credit		376,375	575,625
Net operating loss carryforwards in various foreign jurisdictions		1,549,745
Repatriation transition tax expense		6,000	133,366
Accumulated earnings		177,000	1,936,000
TCJA revaluation of deferred tax assets and liabilities				106,107
Belgium tax reform, income tax expense (benefit)			44,439
Gross unrecognized tax benefits		1,260,970	1,330,713	65,631
Unrecognized tax benefits that would impact effective tax rate		29,420
Interest and penalties		12,555	7,184
Accrued/(reversed) interest and penalties		5,368	(1,085)	$ 165
Expected decrease in unrecognized tax benefits within next twelve months		6,772
Luxembourg
Income Taxes [Line Items]
Net operating loss carryforwards in various foreign jurisdictions		$ 1,224,545	$ 1,298,737
Domestic tax authority
Income Taxes [Line Items]
Effective income tax rate		36.60%	28.70%	43.10%
Foreign tax authority
Income Taxes [Line Items]
Effective income tax rate		(9.40%)	11.00%	3.20%
Foreign tax authority | Tax year 2005 | Belgium
Income Taxes [Line Items]
Foreign tax assessment | €					€ 46,135
Foreign tax authority | Tax year 2006 | Belgium
Income Taxes [Line Items]
Foreign tax assessment | €					38,817
Foreign tax authority | Tax year 2007 | Belgium
Income Taxes [Line Items]
Foreign tax assessment | €					39,635
Foreign tax authority | Tax year 2008 | Belgium
Income Taxes [Line Items]
Foreign tax assessment | €					30,131
Foreign tax authority | Tax year 2009 | Belgium
Income Taxes [Line Items]
Foreign tax assessment | €					35,567
Foreign tax authority | Tax year 2010 | Belgium
Income Taxes [Line Items]
Foreign tax assessment | €					€ 43,117
Foreign tax authority | Tax year 2011 | Belgium
Income Taxes [Line Items]
Foreign tax assessment | €	€ 40,617
Foreign tax authority | Tax year 2012 | Belgium
Income Taxes [Line Items]
Foreign tax assessment | €	39,732
Foreign tax authority | Tax year 2013 | Belgium
Income Taxes [Line Items]
Foreign tax assessment | €	11,358
Foreign tax authority | Tax year 2014 | Belgium
Income Taxes [Line Items]
Foreign tax assessment | €	23,919
Foreign tax authority | Tax year 2015 | Belgium
Income Taxes [Line Items]
Foreign tax assessment | €	30,610
Foreign tax authority | Tax year 2016 | Belgium
Income Taxes [Line Items]
Foreign tax assessment | €	93,145
Foreign tax authority | Tax year 2017 | Belgium
Income Taxes [Line Items]
Foreign tax assessment | €	€ 79,933
State
Income Taxes [Line Items]
Net operating loss carryforwards and tax credit		$ 51,175
Tax Rate Changes, Foreign Currency Translations, and Other Activities
Income Taxes [Line Items]
Increase (decrease) in the valuation allowance		32,650
Restructuring Charges
Income Taxes [Line Items]
Deferred tax benefit related to tax basis of intangible assets		136,194
Foreign subsidiary and state net operating losses and tax credits
Income Taxes [Line Items]
Increase (decrease) in the valuation allowance			$ 15,357
State deferred tax assets
Income Taxes [Line Items]
Valuation allowance against deferred tax asset		31,349
Operating loss carryforward, foreign jurisdiction
Income Taxes [Line Items]
Valuation allowance against deferred tax asset		200,847
Restructuring Charges
Income Taxes [Line Items]
Current tax liability		148,240
Deferred tax asset resulting from restructuring		136,194
Increase (decrease) in the valuation allowance		$ 148,240