Revenue from Contracts with Customers (Impact of ASC 606 on Income Statement) (Details) - USD ($)	12 Months Ended
	Sep. 30, 2019	Sep. 30, 2018	Sep. 30, 2017
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Revenue	$ 1,255,631,000	$ 1,241,824,000	$ 1,164,039,000
Cost of revenue	325,378,000	326,502,000	328,502,000
Gross margin	930,253,000	915,322,000	835,537,000
Sales and marketing	417,449,000	414,764,000	372,702,000
Research and development	246,888,000	249,786,000	236,028,000
General and administrative	127,919,000	143,045,000	144,991,000
Amortization of acquired intangible assets	23,841,000	31,350,000	32,108,000
Restructuring and other charges, net	51,114,000	3,764,000	7,942,000
Total operating expenses	867,211,000	842,709,000	793,771,000
Operating income	63,042,000	72,613,000	41,766,000
Interest expense	(43,047,000)	(41,673,000)	(42,400,000)
Other income (expense), net	305,000	(2,284,000)	(772,000)
Income before income taxes	20,300,000	28,656,000	(1,406,000)
Provision (benefit) for income taxes	47,760,000	(23,331,000)	(7,645,000)
Net income (loss)	(27,460,000)	51,987,000	6,239,000
Calculated under Revenue Guidance in Effect before Topic 606 [Member]
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Revenue	1,311,494,000	1,241,824,000	1,164,039,000
Cost of revenue	318,154,000
Gross margin	993,340,000
Sales and marketing	441,958,000
Research and development	246,888,000
General and administrative	127,919,000
Amortization of acquired intangible assets	23,841,000
Restructuring and other charges, net	51,114,000
Total operating expenses	891,720,000
Operating income	101,620,000
Interest expense	(43,047,000)
Other income (expense), net	131,000
Income before income taxes	58,704,000
Provision (benefit) for income taxes	55,725,000
Net income (loss)	2,979,000
Software
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Revenue	1,088,100,000	1,088,487,000	987,316,000
Cost of revenue	185,414,000	182,843,000	177,772,000
Software | Calculated under Revenue Guidance in Effect before Topic 606 [Member]
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Revenue	1,150,818,000	1,088,487,000	987,316,000
Cost of revenue	183,218,000
Support and cloud services
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Revenue	763,700,000	559,222,000	630,990,000
Cost of revenue	133,478,000	135,106,000	110,931,000
Support and cloud services | Calculated under Revenue Guidance in Effect before Topic 606 [Member]
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Revenue	484,048,000
Cost of revenue	132,987,000
License
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Revenue	324,400,000	529,265,000	356,326,000
Cost of revenue	51,936,000	47,737,000	66,841,000
License | Calculated under Revenue Guidance in Effect before Topic 606 [Member]
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Revenue	666,770,000
Cost of revenue	50,231,000
Professional services
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Revenue	167,531,000	153,337,000	176,723,000
Cost of revenue	139,964,000	143,659,000	150,730,000
Professional services | Calculated under Revenue Guidance in Effect before Topic 606 [Member]
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Revenue	160,676,000	$ 153,337,000	$ 176,723,000
Cost of revenue	134,936,000
Accounting Standards Update 2014-09 [Member] | License
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Revenue	215,000,000.0
Revenue on new and renewal bookings	$ 153,500,000