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Simplifying (11 + n)(10 + n)(9 + n)(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 Multiply (11 + n) * (10 + n) (11(10 + n) + n(10 + n))(9 + n)(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 ((10 * 11 + n * 11) + n(10 + n))(9 + n)(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 ((110 + 11n) + n(10 + n))(9 + n)(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 (110 + 11n + (10 * n + n * n))(9 + n)(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 (110 + 11n + (10n + n2))(9 + n)(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 Combine like terms: 11n + 10n = 21n (110 + 21n + n2)(9 + n)(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 Multiply (110 + 21n + n2) * (9 + n) (110(9 + n) + 21n * (9 + n) + n2(9 + n))(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 ((9 * 110 + n * 110) + 21n * (9 + n) + n2(9 + n))(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 ((990 + 110n) + 21n * (9 + n) + n2(9 + n))(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 (990 + 110n + (9 * 21n + n * 21n) + n2(9 + n))(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 (990 + 110n + (189n + 21n2) + n2(9 + n))(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 (990 + 110n + 189n + 21n2 + (9 * n2 + n * n2))(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 (990 + 110n + 189n + 21n2 + (9n2 + n3))(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 Combine like terms: 110n + 189n = 299n (990 + 299n + 21n2 + 9n2 + n3)(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 Combine like terms: 21n2 + 9n2 = 30n2 (990 + 299n + 30n2 + n3)(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 Multiply (990 + 299n + 30n2 + n3) * (8 + n) (990(8 + n) + 299n * (8 + n) + 30n2 * (8 + n) + n3(8 + n))(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 ((8 * 990 + n * 990) + 299n * (8 + n) + 30n2 * (8 + n) + n3(8 + n))(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 ((7920 + 990n) + 299n * (8 + n) + 30n2 * (8 + n) + n3(8 + n))(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 (7920 + 990n + (8 * 299n + n * 299n) + 30n2 * (8 + n) + n3(8 + n))(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 (7920 + 990n + (2392n + 299n2) + 30n2 * (8 + n) + n3(8 + n))(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 (7920 + 990n + 2392n + 299n2 + (8 * 30n2 + n * 30n2) + n3(8 + n))(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 (7920 + 990n + 2392n + 299n2 + (240n2 + 30n3) + n3(8 + n))(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 (7920 + 990n + 2392n + 299n2 + 240n2 + 30n3 + (8 * n3 + n * n3))(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 (7920 + 990n + 2392n + 299n2 + 240n2 + 30n3 + (8n3 + n4))(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 Combine like terms: 990n + 2392n = 3382n (7920 + 3382n + 299n2 + 240n2 + 30n3 + 8n3 + n4)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 Combine like terms: 299n2 + 240n2 = 539n2 (7920 + 3382n + 539n2 + 30n3 + 8n3 + n4)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 Combine like terms: 30n3 + 8n3 = 38n3 (7920 + 3382n + 539n2 + 38n3 + n4)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 Multiply (7920 + 3382n + 539n2 + 38n3 + n4) * (7 + n) (7920(7 + n) + 3382n * (7 + n) + 539n2 * (7 + n) + 38n3 * (7 + n) + n4(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 ((7 * 7920 + n * 7920) + 3382n * (7 + n) + 539n2 * (7 + n) + 38n3 * (7 + n) + n4(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 ((55440 + 7920n) + 3382n * (7 + n) + 539n2 * (7 + n) + 38n3 * (7 + n) + n4(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 (55440 + 7920n + (7 * 3382n + n * 3382n) + 539n2 * (7 + n) + 38n3 * (7 + n) + n4(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 (55440 + 7920n + (23674n + 3382n2) + 539n2 * (7 + n) + 38n3 * (7 + n) + n4(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 (55440 + 7920n + 23674n + 3382n2 + (7 * 539n2 + n * 539n2) + 38n3 * (7 + n) + n4(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 (55440 + 7920n + 23674n + 3382n2 + (3773n2 + 539n3) + 38n3 * (7 + n) + n4(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 (55440 + 7920n + 23674n + 3382n2 + 3773n2 + 539n3 + (7 * 38n3 + n * 38n3) + n4(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 (55440 + 7920n + 23674n + 3382n2 + 3773n2 + 539n3 + (266n3 + 38n4) + n4(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 (55440 + 7920n + 23674n + 3382n2 + 3773n2 + 539n3 + 266n3 + 38n4 + (7 * n4 + n * n4))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 (55440 + 7920n + 23674n + 3382n2 + 3773n2 + 539n3 + 266n3 + 38n4 + (7n4 + n5))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 Combine like terms: 7920n + 23674n = 31594n (55440 + 31594n + 3382n2 + 3773n2 + 539n3 + 266n3 + 38n4 + 7n4 + n5)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 Combine like terms: 3382n2 + 3773n2 = 7155n2 (55440 + 31594n + 7155n2 + 539n3 + 266n3 + 38n4 + 7n4 + n5)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 Combine like terms: 539n3 + 266n3 = 805n3 (55440 + 31594n + 7155n2 + 805n3 + 38n4 + 7n4 + n5)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 Combine like terms: 38n4 + 7n4 = 45n4 (55440 + 31594n + 7155n2 + 805n3 + 45n4 + n5)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n) = 0 Multiply (55440 + 31594n + 7155n2 + 805n3 + 45n4 + n5) * (6 + n) (55440(6 + n) + 31594n * (6 + n) + 7155n2 * (6 + n) + 805n3 * (6 + n) + 45n4 * (6 + n) + n5(6 + n))(5 + n)(4 + n)(3 + n)(2 + n) = 0 ((6 * 55440 + n * 55440) + 31594n * (6 + n) + 7155n2 * (6 + n) + 805n3 * (6 + n) + 45n4 * (6 + n) + n5(6 + n))(5 + n)(4 + n)(3 + n)(2 + n) = 0 ((332640 + 55440n) + 31594n * (6 + n) + 7155n2 * (6 + n) + 805n3 * (6 + n) + 45n4 * (6 + n) + n5(6 + n))(5 + n)(4 + n)(3 + n)(2 + n) = 0 (332640 + 55440n + (6 * 31594n + n * 31594n) + 7155n2 * (6 + n) + 805n3 * (6 + n) + 45n4 * (6 + n) + n5(6 + n))(5 + n)(4 + n)(3 + n)(2 + n) = 0 (332640 + 55440n + (189564n + 31594n2) + 7155n2 * (6 + n) + 805n3 * (6 + n) + 45n4 * (6 + n) + n5(6 + n))(5 + n)(4 + n)(3 + n)(2 + n) = 0 (332640 + 55440n + 189564n + 31594n2 + (6 * 7155n2 + n * 7155n2) + 805n3 * (6 + n) + 45n4 * (6 + n) + n5(6 + n))(5 + n)(4 + n)(3 + n)(2 + n) = 0 (332640 + 55440n + 189564n + 31594n2 + (42930n2 + 7155n3) + 805n3 * (6 + n) + 45n4 * (6 + n) + n5(6 + n))(5 + n)(4 + n)(3 + n)(2 + n) = 0 (332640 + 55440n + 189564n + 31594n2 + 42930n2 + 7155n3 + (6 * 805n3 + n * 805n3) + 45n4 * (6 + n) + n5(6 + n))(5 + n)(4 + n)(3 + n)(2 + n) = 0 (332640 + 55440n + 189564n + 31594n2 + 42930n2 + 7155n3 + (4830n3 + 805n4) + 45n4 * (6 + n) + n5(6 + n))(5 + n)(4 + n)(3 + n)(2 + n) = 0 (332640 + 55440n + 189564n + 31594n2 + 42930n2 + 7155n3 + 4830n3 + 805n4 + (6 * 45n4 + n * 45n4) + n5(6 + n))(5 + n)(4 + n)(3 + n)(2 + n) = 0 (332640 + 55440n + 189564n + 31594n2 + 42930n2 + 7155n3 + 4830n3 + 805n4 + (270n4 + 45n5) + n5(6 + n))(5 + n)(4 + n)(3 + n)(2 + n) = 0 (332640 + 55440n + 189564n + 31594n2 + 42930n2 + 7155n3 + 4830n3 + 805n4 + 270n4 + 45n5 + (6 * n5 + n * n5))(5 + n)(4 + n)(3 + n)(2 + n) = 0 (332640 + 55440n + 189564n + 31594n2 + 42930n2 + 7155n3 + 4830n3 + 805n4 + 270n4 + 45n5 + (6n5 + n6))(5 + n)(4 + n)(3 + n)(2 + n) = 0 Combine like terms: 55440n + 189564n = 245004n (332640 + 245004n + 31594n2 + 42930n2 + 7155n3 + 4830n3 + 805n4 + 270n4 + 45n5 + 6n5 + n6)(5 + n)(4 + n)(3 + n)(2 + n) = 0 Combine like terms: 31594n2 + 42930n2 = 74524n2 (332640 + 245004n + 74524n2 + 7155n3 + 4830n3 + 805n4 + 270n4 + 45n5 + 6n5 + n6)(5 + n)(4 + n)(3 + n)(2 + n) = 0 Combine like terms: 7155n3 + 4830n3 = 11985n3 (332640 + 245004n + 74524n2 + 11985n3 + 805n4 + 270n4 + 45n5 + 6n5 + n6)(5 + n)(4 + n)(3 + n)(2 + n) = 0 Combine like terms: 805n4 + 270n4 = 1075n4 (332640 + 245004n + 74524n2 + 11985n3 + 1075n4 + 45n5 + 6n5 + n6)(5 + n)(4 + n)(3 + n)(2 + n) = 0 Combine like terms: 45n5 + 6n5 = 51n5 (332640 + 245004n + 74524n2 + 11985n3 + 1075n4 + 51n5 + n6)(5 + n)(4 + n)(3 + n)(2 + n) = 0 Multiply (332640 + 245004n + 74524n2 + 11985n3 + 1075n4 + 51n5 + n6) * (5 + n) (332640(5 + n) + 245004n * (5 + n) + 74524n2 * (5 + n) + 11985n3 * (5 + n) + 1075n4 * (5 + n) + 51n5 * (5 + n) + n6(5 + n))(4 + n)(3 + n)(2 + n) = 0 ((5 * 332640 + n * 332640) + 245004n * (5 + n) + 74524n2 * (5 + n) + 11985n3 * (5 + n) + 1075n4 * (5 + n) + 51n5 * (5 + n) + n6(5 + n))(4 + n)(3 + n)(2 + n) = 0 ((1663200 + 332640n) + 245004n * (5 + n) + 74524n2 * (5 + n) + 11985n3 * (5 + n) + 1075n4 * (5 + n) + 51n5 * (5 + n) + n6(5 + n))(4 + n)(3 + n)(2 + n) = 0 (1663200 + 332640n + (5 * 245004n + n * 245004n) + 74524n2 * (5 + n) + 11985n3 * (5 + n) + 1075n4 * (5 + n) + 51n5 * (5 + n) + n6(5 + n))(4 + n)(3 + n)(2 + n) = 0 (1663200 + 332640n + (1225020n + 245004n2) + 74524n2 * (5 + n) + 11985n3 * (5 + n) + 1075n4 * (5 + n) + 51n5 * (5 + n) + n6(5 + n))(4 + n)(3 + n)(2 + n) = 0 (1663200 + 332640n + 1225020n + 245004n2 + (5 * 74524n2 + n * 74524n2) + 11985n3 * (5 + n) + 1075n4 * (5 + n) + 51n5 * (5 + n) + n6(5 + n))(4 + n)(3 + n)(2 + n) = 0 (1663200 + 332640n + 1225020n + 245004n2 + (372620n2 + 74524n3) + 11985n3 * (5 + n) + 1075n4 * (5 + n) + 51n5 * (5 + n) + n6(5 + n))(4 + n)(3 + n)(2 + n) = 0 (1663200 + 332640n + 1225020n + 245004n2 + 372620n2 + 74524n3 + (5 * 11985n3 + n * 11985n3) + 1075n4 * (5 + n) + 51n5 * (5 + n) + n6(5 + n))(4 + n)(3 + n)(2 + n) = 0 (1663200 + 332640n + 1225020n + 245004n2 + 372620n2 + 74524n3 + (59925n3 + 11985n4) + 1075n4 * (5 + n) + 51n5 * (5 + n) + n6(5 + n))(4 + n)(3 + n)(2 + n) = 0 (1663200 + 332640n + 1225020n + 245004n2 + 372620n2 + 74524n3 + 59925n3 + 11985n4 + (5 * 1075n4 + n * 1075n4) + 51n5 * (5 + n) + n6(5 + n))(4 + n)(3 + n)(2 + n) = 0 (1663200 + 332640n + 1225020n + 245004n2 + 372620n2 + 74524n3 + 59925n3 + 11985n4 + (5375n4 + 1075n5) + 51n5 * (5 + n) + n6(5 + n))(4 + n)(3 + n)(2 + n) = 0 (1663200 + 332640n + 1225020n + 245004n2 + 372620n2 + 74524n3 + 59925n3 + 11985n4 + 5375n4 + 1075n5 + (5 * 51n5 + n * 51n5) + n6(5 + n))(4 + n)(3 + n)(2 + n) = 0 (1663200 + 332640n + 1225020n + 245004n2 + 372620n2 + 74524n3 + 59925n3 + 11985n4 + 5375n4 + 1075n5 + (255n5 + 51n6) + n6(5 + n))(4 + n)(3 + n)(2 + n) = 0 (1663200 + 332640n + 1225020n + 245004n2 + 372620n2 + 74524n3 + 59925n3 + 11985n4 + 5375n4 + 1075n5 + 255n5 + 51n6 + (5 * n6 + n * n6))(4 + n)(3 + n)(2 + n) = 0 (1663200 + 332640n + 1225020n + 245004n2 + 372620n2 + 74524n3 + 59925n3 + 11985n4 + 5375n4 + 1075n5 + 255n5 + 51n6 + (5n6 + n7))(4 + n)(3 + n)(2 + n) = 0 Combine like terms: 332640n + 1225020n = 1557660n (1663200 + 1557660n + 245004n2 + 372620n2 + 74524n3 + 59925n3 + 11985n4 + 5375n4 + 1075n5 + 255n5 + 51n6 + 5n6 + n7)(4 + n)(3 + n)(2 + n) = 0 Combine like terms: 245004n2 + 372620n2 = 617624n2 (1663200 + 1557660n + 617624n2 + 74524n3 + 59925n3 + 11985n4 + 5375n4 + 1075n5 + 255n5 + 51n6 + 5n6 + n7)(4 + n)(3 + n)(2 + n) = 0 Combine like terms: 74524n3 + 59925n3 = 134449n3 (1663200 + 1557660n + 617624n2 + 134449n3 + 11985n4 + 5375n4 + 1075n5 + 255n5 + 51n6 + 5n6 + n7)(4 + n)(3 + n)(2 + n) = 0 Combine like terms: 11985n4 + 5375n4 = 17360n4 (1663200 + 1557660n + 617624n2 + 134449n3 + 17360n4 + 1075n5 + 255n5 + 51n6 + 5n6 + n7)(4 + n)(3 + n)(2 + n) = 0 Combine like terms: 1075n5 + 255n5 = 1330n5 (1663200 + 1557660n + 617624n2 + 134449n3 + 17360n4 + 1330n5 + 51n6 + 5n6 + n7)(4 + n)(3 + n)(2 + n) = 0 Combine like terms: 51n6 + 5n6 = 56n6 (1663200 + 1557660n + 617624n2 + 134449n3 + 17360n4 + 1330n5 + 56n6 + n7)(4 + n)(3 + n)(2 + n) = 0 Multiply (1663200 + 1557660n + 617624n2 + 134449n3 + 17360n4 + 1330n5 + 56n6 + n7) * (4 + n) (1663200(4 + n) + 1557660n * (4 + n) + 617624n2 * (4 + n) + 134449n3 * (4 + n) + 17360n4 * (4 + n) + 1330n5 * (4 + n) + 56n6 * (4 + n) + n7(4 + n))(3 + n)(2 + n) = 0 ((4 * 1663200 + n * 1663200) + 1557660n * (4 + n) + 617624n2 * (4 + n) + 134449n3 * (4 + n) + 17360n4 * (4 + n) + 1330n5 * (4 + n) + 56n6 * (4 + n) + n7(4 + n))(3 + n)(2 + n) = 0 ((6652800 + 1663200n) + 1557660n * (4 + n) + 617624n2 * (4 + n) + 134449n3 * (4 + n) + 17360n4 * (4 + n) + 1330n5 * (4 + n) + 56n6 * (4 + n) + n7(4 + n))(3 + n)(2 + n) = 0 (6652800 + 1663200n + (4 * 1557660n + n * 1557660n) + 617624n2 * (4 + n) + 134449n3 * (4 + n) + 17360n4 * (4 + n) + 1330n5 * (4 + n) + 56n6 * (4 + n) + n7(4 + n))(3 + n)(2 + n) = 0 (6652800 + 1663200n + (6230640n + 1557660n2) + 617624n2 * (4 + n) + 134449n3 * (4 + n) + 17360n4 * (4 + n) + 1330n5 * (4 + n) + 56n6 * (4 + n) + n7(4 + n))(3 + n)(2 + n) = 0 (6652800 + 1663200n + 6230640n + 1557660n2 + (4 * 617624n2 + n * 617624n2) + 134449n3 * (4 + n) + 17360n4 * (4 + n) + 1330n5 * (4 + n) + 56n6 * (4 + n) + n7(4 + n))(3 + n)(2 + n) = 0 (6652800 + 1663200n + 6230640n + 1557660n2 + (2470496n2 + 617624n3) + 134449n3 * (4 + n) + 17360n4 * (4 + n) + 1330n5 * (4 + n) + 56n6 * (4 + n) + n7(4 + n))(3 + n)(2 + n) = 0 (6652800 + 1663200n + 6230640n + 1557660n2 + 2470496n2 + 617624n3 + (4 * 134449n3 + n * 134449n3) + 17360n4 * (4 + n) + 1330n5 * (4 + n) + 56n6 * (4 + n) + n7(4 + n))(3 + n)(2 + n) = 0 (6652800 + 1663200n + 6230640n + 1557660n2 + 2470496n2 + 617624n3 + (537796n3 + 134449n4) + 17360n4 * (4 + n) + 1330n5 * (4 + n) + 56n6 * (4 + n) + n7(4 + n))(3 + n)(2 + n) = 0 (6652800 + 1663200n + 6230640n + 1557660n2 + 2470496n2 + 617624n3 + 537796n3 + 134449n4 + (4 * 17360n4 + n * 17360n4) + 1330n5 * (4 + n) + 56n6 * (4 + n) + n7(4 + n))(3 + n)(2 + n) = 0 (6652800 + 1663200n + 6230640n + 1557660n2 + 2470496n2 + 617624n3 + 537796n3 + 134449n4 + (69440n4 + 17360n5) + 1330n5 * (4 + n) + 56n6 * (4 + n) + n7(4 + n))(3 + n)(2 + n) = 0 (6652800 + 1663200n + 6230640n + 1557660n2 + 2470496n2 + 617624n3 + 537796n3 + 134449n4 + 69440n4 + 17360n5 + (4 * 1330n5 + n * 1330n5) + 56n6 * (4 + n) + n7(4 + n))(3 + n)(2 + n) = 0 (6652800 + 1663200n + 6230640n + 1557660n2 + 2470496n2 + 617624n3 + 537796n3 + 134449n4 + 69440n4 + 17360n5 + (5320n5 + 1330n6) + 56n6 * (4 + n) + n7(4 + n))(3 + n)(2 + n) = 0 (6652800 + 1663200n + 6230640n + 1557660n2 + 2470496n2 + 617624n3 + 537796n3 + 134449n4 + 69440n4 + 17360n5 + 5320n5 + 1330n6 + (4 * 56n6 + n * 56n6) + n7(4 + n))(3 + n)(2 + n) = 0 (6652800 + 1663200n + 6230640n + 1557660n2 + 2470496n2 + 617624n3 + 537796n3 + 134449n4 + 69440n4 + 17360n5 + 5320n5 + 1330n6 + (224n6 + 56n7) + n7(4 + n))(3 + n)(2 + n) = 0 (6652800 + 1663200n + 6230640n + 1557660n2 + 2470496n2 + 617624n3 + 537796n3 + 134449n4 + 69440n4 + 17360n5 + 5320n5 + 1330n6 + 224n6 + 56n7 + (4 * n7 + n * n7))(3 + n)(2 + n) = 0 (6652800 + 1663200n + 6230640n + 1557660n2 + 2470496n2 + 617624n3 + 537796n3 + 134449n4 + 69440n4 + 17360n5 + 5320n5 + 1330n6 + 224n6 + 56n7 + (4n7 + n8))(3 + n)(2 + n) = 0 Combine like terms: 1663200n + 6230640n = 7893840n (6652800 + 7893840n + 1557660n2 + 2470496n2 + 617624n3 + 537796n3 + 134449n4 + 69440n4 + 17360n5 + 5320n5 + 1330n6 + 224n6 + 56n7 + 4n7 + n8)(3 + n)(2 + n) = 0 Combine like terms: 1557660n2 + 2470496n2 = 4028156n2 (6652800 + 7893840n + 4028156n2 + 617624n3 + 537796n3 + 134449n4 + 69440n4 + 17360n5 + 5320n5 + 1330n6 + 224n6 + 56n7 + 4n7 + n8)(3 + n)(2 + n) = 0 Combine like terms: 617624n3 + 537796n3 = 1155420n3 (6652800 + 7893840n + 4028156n2 + 1155420n3 + 134449n4 + 69440n4 + 17360n5 + 5320n5 + 1330n6 + 224n6 + 56n7 + 4n7 + n8)(3 + n)(2 + n) = 0 Combine like terms: 134449n4 + 69440n4 = 203889n4 (6652800 + 7893840n + 4028156n2 + 1155420n3 + 203889n4 + 17360n5 + 5320n5 + 1330n6 + 224n6 + 56n7 + 4n7 + n8)(3 + n)(2 + n) = 0 Combine like terms: 17360n5 + 5320n5 = 22680n5 (6652800 + 7893840n + 4028156n2 + 1155420n3 + 203889n4 + 22680n5 + 1330n6 + 224n6 + 56n7 + 4n7 + n8)(3 + n)(2 + n) = 0 Combine like terms: 1330n6 + 224n6 = 1554n6 (6652800 + 7893840n + 4028156n2 + 1155420n3 + 203889n4 + 22680n5 + 1554n6 + 56n7 + 4n7 + n8)(3 + n)(2 + n) = 0 Combine like terms: 56n7 + 4n7 = 60n7 (6652800 + 7893840n + 4028156n2 + 1155420n3 + 203889n4 + 22680n5 + 1554n6 + 60n7 + n8)(3 + n)(2 + n) = 0 Multiply (6652800 + 7893840n + 4028156n2 + 1155420n3 + 203889n4 + 22680n5 + 1554n6 + 60n7 + n8) * (3 + n) (6652800(3 + n) + 7893840n * (3 + n) + 4028156n2 * (3 + n) + 1155420n3 * (3 + n) + 203889n4 * (3 + n) + 22680n5 * (3 + n) + 1554n6 * (3 + n) + 60n7 * (3 + n) + n8(3 + n))(2 + n) = 0 ((3 * 6652800 + n * 6652800) + 7893840n * (3 + n) + 4028156n2 * (3 + n) + 1155420n3 * (3 + n) + 203889n4 * (3 + n) + 22680n5 * (3 + n) + 1554n6 * (3 + n) + 60n7 * (3 + n) + n8(3 + n))(2 + n) = 0 ((19958400 + 6652800n) + 7893840n * (3 + n) + 4028156n2 * (3 + n) + 1155420n3 * (3 + n) + 203889n4 * (3 + n) + 22680n5 * (3 + n) + 1554n6 * (3 + n) + 60n7 * (3 + n) + n8(3 + n))(2 + n) = 0 (19958400 + 6652800n + (3 * 7893840n + n * 7893840n) + 4028156n2 * (3 + n) + 1155420n3 * (3 + n) + 203889n4 * (3 + n) + 22680n5 * (3 + n) + 1554n6 * (3 + n) + 60n7 * (3 + n) + n8(3 + n))(2 + n) = 0 (19958400 + 6652800n + (23681520n + 7893840n2) + 4028156n2 * (3 + n) + 1155420n3 * (3 + n) + 203889n4 * (3 + n) + 22680n5 * (3 + n) + 1554n6 * (3 + n) + 60n7 * (3 + n) + n8(3 + n))(2 + n) = 0 (19958400 + 6652800n + 23681520n + 7893840n2 + (3 * 4028156n2 + n * 4028156n2) + 1155420n3 * (3 + n) + 203889n4 * (3 + n) + 22680n5 * (3 + n) + 1554n6 * (3 + n) + 60n7 * (3 + n) + n8(3 + n))(2 + n) = 0 (19958400 + 6652800n + 23681520n + 7893840n2 + (12084468n2 + 4028156n3) + 1155420n3 * (3 + n) + 203889n4 * (3 + n) + 22680n5 * (3 + n) + 1554n6 * (3 + n) + 60n7 * (3 + n) + n8(3 + n))(2 + n) = 0 (19958400 + 6652800n + 23681520n + 7893840n2 + 12084468n2 + 4028156n3 + (3 * 1155420n3 + n * 1155420n3) + 203889n4 * (3 + n) + 22680n5 * (3 + n) + 1554n6 * (3 + n) + 60n7 * (3 + n) + n8(3 + n))(2 + n) = 0 (19958400 + 6652800n + 23681520n + 7893840n2 + 12084468n2 + 4028156n3 + (3466260n3 + 1155420n4) + 203889n4 * (3 + n) + 22680n5 * (3 + n) + 1554n6 * (3 + n) + 60n7 * (3 + n) + n8(3 + n))(2 + n) = 0 (19958400 + 6652800n + 23681520n + 7893840n2 + 12084468n2 + 4028156n3 + 3466260n3 + 1155420n4 + (3 * 203889n4 + n * 203889n4) + 22680n5 * (3 + n) + 1554n6 * (3 + n) + 60n7 * (3 + n) + n8(3 + n))(2 + n) = 0 (19958400 + 6652800n + 23681520n + 7893840n2 + 12084468n2 + 4028156n3 + 3466260n3 + 1155420n4 + (611667n4 + 203889n5) + 22680n5 * (3 + n) + 1554n6 * (3 + n) + 60n7 * (3 + n) + n8(3 + n))(2 + n) = 0 (19958400 + 6652800n + 23681520n + 7893840n2 + 12084468n2 + 4028156n3 + 3466260n3 + 1155420n4 + 611667n4 + 203889n5 + (3 * 22680n5 + n * 22680n5) + 1554n6 * (3 + n) + 60n7 * (3 + n) + n8(3 + n))(2 + n) = 0 (19958400 + 6652800n + 23681520n + 7893840n2 + 12084468n2 + 4028156n3 + 3466260n3 + 1155420n4 + 611667n4 + 203889n5 + (68040n5 + 22680n6) + 1554n6 * (3 + n) + 60n7 * (3 + n) + n8(3 + n))(2 + n) = 0 (19958400 + 6652800n + 23681520n + 7893840n2 + 12084468n2 + 4028156n3 + 3466260n3 + 1155420n4 + 611667n4 + 203889n5 + 68040n5 + 22680n6 + (3 * 1554n6 + n * 1554n6) + 60n7 * (3 + n) + n8(3 + n))(2 + n) = 0 (19958400 + 6652800n + 23681520n + 7893840n2 + 12084468n2 + 4028156n3 + 3466260n3 + 1155420n4 + 611667n4 + 203889n5 + 68040n5 + 22680n6 + (4662n6 + 1554n7) + 60n7 * (3 + n) + n8(3 + n))(2 + n) = 0 (19958400 + 6652800n + 23681520n + 7893840n2 + 12084468n2 + 4028156n3 + 3466260n3 + 1155420n4 + 611667n4 + 203889n5 + 68040n5 + 22680n6 + 4662n6 + 1554n7 + (3 * 60n7 + n * 60n7) + n8(3 + n))(2 + n) = 0 (19958400 + 6652800n + 23681520n + 7893840n2 + 12084468n2 + 4028156n3 + 3466260n3 + 1155420n4 + 611667n4 + 203889n5 + 68040n5 + 22680n6 + 4662n6 + 1554n7 + (180n7 + 60n8) + n8(3 + n))(2 + n) = 0 (19958400 + 6652800n + 23681520n + 7893840n2 + 12084468n2 + 4028156n3 + 3466260n3 + 1155420n4 + 611667n4 + 203889n5 + 68040n5 + 22680n6 + 4662n6 + 1554n7 + 180n7 + 60n8 + (3 * n8 + n * n8))(2 + n) = 0 (19958400 + 6652800n + 23681520n + 7893840n2 + 12084468n2 + 4028156n3 + 3466260n3 + 1155420n4 + 611667n4 + 203889n5 + 68040n5 + 22680n6 + 4662n6 + 1554n7 + 180n7 + 60n8 + (3n8 + n9))(2 + n) = 0 Combine like terms: 6652800n + 23681520n = 30334320n (19958400 + 30334320n + 7893840n2 + 12084468n2 + 4028156n3 + 3466260n3 + 1155420n4 + 611667n4 + 203889n5 + 68040n5 + 22680n6 + 4662n6 + 1554n7 + 180n7 + 60n8 + 3n8 + n9)(2 + n) = 0 Combine like terms: 7893840n2 + 12084468n2 = 19978308n2 (19958400 + 30334320n + 19978308n2 + 4028156n3 + 3466260n3 + 1155420n4 + 611667n4 + 203889n5 + 68040n5 + 22680n6 + 4662n6 + 1554n7 + 180n7 + 60n8 + 3n8 + n9)(2 + n) = 0 Combine like terms: 4028156n3 + 3466260n3 = 7494416n3 (19958400 + 30334320n + 19978308n2 + 7494416n3 + 1155420n4 + 611667n4 + 203889n5 + 68040n5 + 22680n6 + 4662n6 + 1554n7 + 180n7 + 60n8 + 3n8 + n9)(2 + n) = 0 Combine like terms: 1155420n4 + 611667n4 = 1767087n4 (19958400 + 30334320n + 19978308n2 + 7494416n3 + 1767087n4 + 203889n5 + 68040n5 + 22680n6 + 4662n6 + 1554n7 + 180n7 + 60n8 + 3n8 + n9)(2 + n) = 0 Combine like terms: 203889n5 + 68040n5 = 271929n5 (19958400 + 30334320n + 19978308n2 + 7494416n3 + 1767087n4 + 271929n5 + 22680n6 + 4662n6 + 1554n7 + 180n7 + 60n8 + 3n8 + n9)(2 + n) = 0 Combine like terms: 22680n6 + 4662n6 = 27342n6 (19958400 + 30334320n + 19978308n2 + 7494416n3 + 1767087n4 + 271929n5 + 27342n6 + 1554n7 + 180n7 + 60n8 + 3n8 + n9)(2 + n) = 0 Combine like terms: 1554n7 + 180n7 = 1734n7 (19958400 + 30334320n + 19978308n2 + 7494416n3 + 1767087n4 + 271929n5 + 27342n6 + 1734n7 + 60n8 + 3n8 + n9)(2 + n) = 0 Combine like terms: 60n8 + 3n8 = 63n8 (19958400 + 30334320n + 19978308n2 + 7494416n3 + 1767087n4 + 271929n5 + 27342n6 + 1734n7 + 63n8 + n9)(2 + n) = 0 Multiply (19958400 + 30334320n + 19978308n2 + 7494416n3 + 1767087n4 + 271929n5 + 27342n6 + 1734n7 + 63n8 + n9) * (2 + n) (19958400(2 + n) + 30334320n * (2 + n) + 19978308n2 * (2 + n) + 7494416n3 * (2 + n) + 1767087n4 * (2 + n) + 271929n5 * (2 + n) + 27342n6 * (2 + n) + 1734n7 * (2 + n) + 63n8 * (2 + n) + n9(2 + n)) = 0 ((2 * 19958400 + n * 19958400) + 30334320n * (2 + n) + 19978308n2 * (2 + n) + 7494416n3 * (2 + n) + 1767087n4 * (2 + n) + 271929n5 * (2 + n) + 27342n6 * (2 + n) + 1734n7 * (2 + n) + 63n8 * (2 + n) + n9(2 + n)) = 0 ((39916800 + 19958400n) + 30334320n * (2 + n) + 19978308n2 * (2 + n) + 7494416n3 * (2 + n) + 1767087n4 * (2 + n) + 271929n5 * (2 + n) + 27342n6 * (2 + n) + 1734n7 * (2 + n) + 63n8 * (2 + n) + n9(2 + n)) = 0 (39916800 + 19958400n + (2 * 30334320n + n * 30334320n) + 19978308n2 * (2 + n) + 7494416n3 * (2 + n) + 1767087n4 * (2 + n) + 271929n5 * (2 + n) + 27342n6 * (2 + n) + 1734n7 * (2 + n) + 63n8 * (2 + n) + n9(2 + n)) = 0 (39916800 + 19958400n + (60668640n + 30334320n2) + 19978308n2 * (2 + n) + 7494416n3 * (2 + n) + 1767087n4 * (2 + n) + 271929n5 * (2 + n) + 27342n6 * (2 + n) + 1734n7 * (2 + n) + 63n8 * (2 + n) + n9(2 + n)) = 0 (39916800 + 19958400n + 60668640n + 30334320n2 + (2 * 19978308n2 + n * 19978308n2) + 7494416n3 * (2 + n) + 1767087n4 * (2 + n) + 271929n5 * (2 + n) + 27342n6 * (2 + n) + 1734n7 * (2 + n) + 63n8 * (2 + n) + n9(2 + n)) = 0 (39916800 + 19958400n + 60668640n + 30334320n2 + (39956616n2 + 19978308n3) + 7494416n3 * (2 + n) + 1767087n4 * (2 + n) + 271929n5 * (2 + n) + 27342n6 * (2 + n) + 1734n7 * (2 + n) + 63n8 * (2 + n) + n9(2 + n)) = 0 (39916800 + 19958400n + 60668640n + 30334320n2 + 39956616n2 + 19978308n3 + (2 * 7494416n3 + n * 7494416n3) + 1767087n4 * (2 + n) + 271929n5 * (2 + n) + 27342n6 * (2 + n) + 1734n7 * (2 + n) + 63n8 * (2 + n) + n9(2 + n)) = 0 (39916800 + 19958400n + 60668640n + 30334320n2 + 39956616n2 + 19978308n3 + (14988832n3 + 7494416n4) + 1767087n4 * (2 + n) + 271929n5 * (2 + n) + 27342n6 * (2 + n) + 1734n7 * (2 + n) + 63n8 * (2 + n) + n9(2 + n)) = 0 (39916800 + 19958400n + 60668640n + 30334320n2 + 39956616n2 + 19978308n3 + 14988832n3 + 7494416n4 + (2 * 1767087n4 + n * 1767087n4) + 271929n5 * (2 + n) + 27342n6 * (2 + n) + 1734n7 * (2 + n) + 63n8 * (2 + n) + n9(2 + n)) = 0 (39916800 + 19958400n + 60668640n + 30334320n2 + 39956616n2 + 19978308n3 + 14988832n3 + 7494416n4 + (3534174n4 + 1767087n5) + 271929n5 * (2 + n) + 27342n6 * (2 + n) + 1734n7 * (2 + n) + 63n8 * (2 + n) + n9(2 + n)) = 0 (39916800 + 19958400n + 60668640n + 30334320n2 + 39956616n2 + 19978308n3 + 14988832n3 + 7494416n4 + 3534174n4 + 1767087n5 + (2 * 271929n5 + n * 271929n5) + 27342n6 * (2 + n) + 1734n7 * (2 + n) + 63n8 * (2 + n) + n9(2 + n)) = 0 (39916800 + 19958400n + 60668640n + 30334320n2 + 39956616n2 + 19978308n3 + 14988832n3 + 7494416n4 + 3534174n4 + 1767087n5 + (543858n5 + 271929n6) + 27342n6 * (2 + n) + 1734n7 * (2 + n) + 63n8 * (2 + n) + n9(2 + n)) = 0 (39916800 + 19958400n + 60668640n + 30334320n2 + 39956616n2 + 19978308n3 + 14988832n3 + 7494416n4 + 3534174n4 + 1767087n5 + 543858n5 + 271929n6 + (2 * 27342n6 + n * 27342n6) + 1734n7 * (2 + n) + 63n8 * (2 + n) + n9(2 + n)) = 0 (39916800 + 19958400n + 60668640n + 30334320n2 + 39956616n2 + 19978308n3 + 14988832n3 + 7494416n4 + 3534174n4 + 1767087n5 + 543858n5 + 271929n6 + (54684n6 + 27342n7) + 1734n7 * (2 + n) + 63n8 * (2 + n) + n9(2 + n)) = 0 (39916800 + 19958400n + 60668640n + 30334320n2 + 39956616n2 + 19978308n3 + 14988832n3 + 7494416n4 + 3534174n4 + 1767087n5 + 543858n5 + 271929n6 + 54684n6 + 27342n7 + (2 * 1734n7 + n * 1734n7) + 63n8 * (2 + n) + n9(2 + n)) = 0 (39916800 + 19958400n + 60668640n + 30334320n2 + 39956616n2 + 19978308n3 + 14988832n3 + 7494416n4 + 3534174n4 + 1767087n5 + 543858n5 + 271929n6 + 54684n6 + 27342n7 + (3468n7 + 1734n8) + 63n8 * (2 + n) + n9(2 + n)) = 0 (39916800 + 19958400n + 60668640n + 30334320n2 + 39956616n2 + 19978308n3 + 14988832n3 + 7494416n4 + 3534174n4 + 1767087n5 + 543858n5 + 271929n6 + 54684n6 + 27342n7 + 3468n7 + 1734n8 + (2 * 63n8 + n * 63n8) + n9(2 + n)) = 0 (39916800 + 19958400n + 60668640n + 30334320n2 + 39956616n2 + 19978308n3 + 14988832n3 + 7494416n4 + 3534174n4 + 1767087n5 + 543858n5 + 271929n6 + 54684n6 + 27342n7 + 3468n7 + 1734n8 + (126n8 + 63n9) + n9(2 + n)) = 0 (39916800 + 19958400n + 60668640n + 30334320n2 + 39956616n2 + 19978308n3 + 14988832n3 + 7494416n4 + 3534174n4 + 1767087n5 + 543858n5 + 271929n6 + 54684n6 + 27342n7 + 3468n7 + 1734n8 + 126n8 + 63n9 + (2 * n9 + n * n9)) = 0 (39916800 + 19958400n + 60668640n + 30334320n2 + 39956616n2 + 19978308n3 + 14988832n3 + 7494416n4 + 3534174n4 + 1767087n5 + 543858n5 + 271929n6 + 54684n6 + 27342n7 + 3468n7 + 1734n8 + 126n8 + 63n9 + (2n9 + n10)) = 0 Combine like terms: 19958400n + 60668640n = 80627040n (39916800 + 80627040n + 30334320n2 + 39956616n2 + 19978308n3 + 14988832n3 + 7494416n4 + 3534174n4 + 1767087n5 + 543858n5 + 271929n6 + 54684n6 + 27342n7 + 3468n7 + 1734n8 + 126n8 + 63n9 + 2n9 + n10) = 0 Combine like terms: 30334320n2 + 39956616n2 = 70290936n2 (39916800 + 80627040n + 70290936n2 + 19978308n3 + 14988832n3 + 7494416n4 + 3534174n4 + 1767087n5 + 543858n5 + 271929n6 + 54684n6 + 27342n7 + 3468n7 + 1734n8 + 126n8 + 63n9 + 2n9 + n10) = 0 Combine like terms: 19978308n3 + 14988832n3 = 34967140n3 (39916800 + 80627040n + 70290936n2 + 34967140n3 + 7494416n4 + 3534174n4 + 1767087n5 + 543858n5 + 271929n6 + 54684n6 + 27342n7 + 3468n7 + 1734n8 + 126n8 + 63n9 + 2n9 + n10) = 0 Combine like terms: 7494416n4 + 3534174n4 = 11028590n4 (39916800 + 80627040n + 70290936n2 + 34967140n3 + 11028590n4 + 1767087n5 + 543858n5 + 271929n6 + 54684n6 + 27342n7 + 3468n7 + 1734n8 + 126n8 + 63n9 + 2n9 + n10) = 0 Combine like terms: 1767087n5 + 543858n5 = 2310945n5 (39916800 + 80627040n + 70290936n2 + 34967140n3 + 11028590n4 + 2310945n5 + 271929n6 + 54684n6 + 27342n7 + 3468n7 + 1734n8 + 126n8 + 63n9 + 2n9 + n10) = 0 Combine like terms: 271929n6 + 54684n6 = 326613n6 (39916800 + 80627040n + 70290936n2 + 34967140n3 + 11028590n4 + 2310945n5 + 326613n6 + 27342n7 + 3468n7 + 1734n8 + 126n8 + 63n9 + 2n9 + n10) = 0 Combine like terms: 27342n7 + 3468n7 = 30810n7 (39916800 + 80627040n + 70290936n2 + 34967140n3 + 11028590n4 + 2310945n5 + 326613n6 + 30810n7 + 1734n8 + 126n8 + 63n9 + 2n9 + n10) = 0 Combine like terms: 1734n8 + 126n8 = 1860n8 (39916800 + 80627040n + 70290936n2 + 34967140n3 + 11028590n4 + 2310945n5 + 326613n6 + 30810n7 + 1860n8 + 63n9 + 2n9 + n10) = 0 Combine like terms: 63n9 + 2n9 = 65n9 (39916800 + 80627040n + 70290936n2 + 34967140n3 + 11028590n4 + 2310945n5 + 326613n6 + 30810n7 + 1860n8 + 65n9 + n10) = 0 Solving 39916800 + 80627040n + 70290936n2 + 34967140n3 + 11028590n4 + 2310945n5 + 326613n6 + 30810n7 + 1860n8 + 65n9 + n10 = 0 Solving for variable 'n'. The solution to this equation could not be determined.
| 25=-3x+10 | | -3(1-7r)=-150 | | 0.7=m-1.8 | | 5r=45-15 | | 4a^2+8ab-12b^2=0 | | -12x=-132 | | -6y-6= | | 6n^2-6n-120=0 | | 2x+x/3=28 | | -158=-10n+2 | | x^2=1.8x | | f^2+11f+18= | | 2x+1/3x=28 | | 158=-10n+2 | | -112=-3(8-2n)+5n | | 5t=45-15 | | -9n+11=-8n-5 | | -25.5=8.5a-2a | | -7x+7=11x-29 | | 11x+6i=-22+(12y)i | | 6-4(6n+7)=102 | | 3x+4y=7xy | | 21=3x-12 | | 9-7n=-19 | | 17.50(p+4)=315 | | 7y-9=3y+7 | | -3+10=12x-4-11x | | 3(x-1)=3x-1+x | | 18x-3x^2=0 | | 0=-a-5+1 | | 80x+1=75x+2 | | 9(n+9)=9 |