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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)(1 + n) * n = 0 Reorder the terms for easier multiplication: n(11 + n)(10 + n)(9 + n)(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Multiply (11 + n) * (10 + n) n(11(10 + n) + n(10 + n))(9 + n)(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n((10 * 11 + n * 11) + n(10 + n))(9 + n)(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n((110 + 11n) + n(10 + n))(9 + n)(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(110 + 11n + (10 * n + n * n))(9 + n)(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(110 + 11n + (10n + n2))(9 + n)(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 11n + 10n = 21n n(110 + 21n + n2)(9 + n)(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Multiply (110 + 21n + n2) * (9 + n) n(110(9 + n) + 21n * (9 + n) + n2(9 + n))(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n((9 * 110 + n * 110) + 21n * (9 + n) + n2(9 + n))(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n((990 + 110n) + 21n * (9 + n) + n2(9 + n))(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(990 + 110n + (9 * 21n + n * 21n) + n2(9 + n))(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(990 + 110n + (189n + 21n2) + n2(9 + n))(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(990 + 110n + 189n + 21n2 + (9 * n2 + n * n2))(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(990 + 110n + 189n + 21n2 + (9n2 + n3))(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 110n + 189n = 299n n(990 + 299n + 21n2 + 9n2 + n3)(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 21n2 + 9n2 = 30n2 n(990 + 299n + 30n2 + n3)(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Multiply (990 + 299n + 30n2 + n3) * (8 + n) 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)(1 + n) = 0 n((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)(1 + n) = 0 n((7920 + 990n) + 299n * (8 + n) + 30n2 * (8 + n) + n3(8 + n))(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(7920 + 990n + (8 * 299n + n * 299n) + 30n2 * (8 + n) + n3(8 + n))(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(7920 + 990n + (2392n + 299n2) + 30n2 * (8 + n) + n3(8 + n))(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(7920 + 990n + 2392n + 299n2 + (8 * 30n2 + n * 30n2) + n3(8 + n))(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(7920 + 990n + 2392n + 299n2 + (240n2 + 30n3) + n3(8 + n))(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(7920 + 990n + 2392n + 299n2 + 240n2 + 30n3 + (8 * n3 + n * n3))(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(7920 + 990n + 2392n + 299n2 + 240n2 + 30n3 + (8n3 + n4))(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 990n + 2392n = 3382n n(7920 + 3382n + 299n2 + 240n2 + 30n3 + 8n3 + n4)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 299n2 + 240n2 = 539n2 n(7920 + 3382n + 539n2 + 30n3 + 8n3 + n4)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 30n3 + 8n3 = 38n3 n(7920 + 3382n + 539n2 + 38n3 + n4)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Multiply (7920 + 3382n + 539n2 + 38n3 + n4) * (7 + n) 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)(1 + n) = 0 n((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)(1 + n) = 0 n((55440 + 7920n) + 3382n * (7 + n) + 539n2 * (7 + n) + 38n3 * (7 + n) + n4(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(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)(1 + n) = 0 n(55440 + 7920n + (23674n + 3382n2) + 539n2 * (7 + n) + 38n3 * (7 + n) + n4(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(55440 + 7920n + 23674n + 3382n2 + (7 * 539n2 + n * 539n2) + 38n3 * (7 + n) + n4(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(55440 + 7920n + 23674n + 3382n2 + (3773n2 + 539n3) + 38n3 * (7 + n) + n4(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(55440 + 7920n + 23674n + 3382n2 + 3773n2 + 539n3 + (7 * 38n3 + n * 38n3) + n4(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(55440 + 7920n + 23674n + 3382n2 + 3773n2 + 539n3 + (266n3 + 38n4) + n4(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(55440 + 7920n + 23674n + 3382n2 + 3773n2 + 539n3 + 266n3 + 38n4 + (7 * n4 + n * n4))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(55440 + 7920n + 23674n + 3382n2 + 3773n2 + 539n3 + 266n3 + 38n4 + (7n4 + n5))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 7920n + 23674n = 31594n n(55440 + 31594n + 3382n2 + 3773n2 + 539n3 + 266n3 + 38n4 + 7n4 + n5)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 3382n2 + 3773n2 = 7155n2 n(55440 + 31594n + 7155n2 + 539n3 + 266n3 + 38n4 + 7n4 + n5)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 539n3 + 266n3 = 805n3 n(55440 + 31594n + 7155n2 + 805n3 + 38n4 + 7n4 + n5)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 38n4 + 7n4 = 45n4 n(55440 + 31594n + 7155n2 + 805n3 + 45n4 + n5)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Multiply (55440 + 31594n + 7155n2 + 805n3 + 45n4 + n5) * (6 + n) 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)(1 + n) = 0 n((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)(1 + n) = 0 n((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)(1 + n) = 0 n(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)(1 + n) = 0 n(332640 + 55440n + (189564n + 31594n2) + 7155n2 * (6 + n) + 805n3 * (6 + n) + 45n4 * (6 + n) + n5(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(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)(1 + n) = 0 n(332640 + 55440n + 189564n + 31594n2 + (42930n2 + 7155n3) + 805n3 * (6 + n) + 45n4 * (6 + n) + n5(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(332640 + 55440n + 189564n + 31594n2 + 42930n2 + 7155n3 + (6 * 805n3 + n * 805n3) + 45n4 * (6 + n) + n5(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(332640 + 55440n + 189564n + 31594n2 + 42930n2 + 7155n3 + (4830n3 + 805n4) + 45n4 * (6 + n) + n5(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(332640 + 55440n + 189564n + 31594n2 + 42930n2 + 7155n3 + 4830n3 + 805n4 + (6 * 45n4 + n * 45n4) + n5(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(332640 + 55440n + 189564n + 31594n2 + 42930n2 + 7155n3 + 4830n3 + 805n4 + (270n4 + 45n5) + n5(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(332640 + 55440n + 189564n + 31594n2 + 42930n2 + 7155n3 + 4830n3 + 805n4 + 270n4 + 45n5 + (6 * n5 + n * n5))(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(332640 + 55440n + 189564n + 31594n2 + 42930n2 + 7155n3 + 4830n3 + 805n4 + 270n4 + 45n5 + (6n5 + n6))(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 55440n + 189564n = 245004n n(332640 + 245004n + 31594n2 + 42930n2 + 7155n3 + 4830n3 + 805n4 + 270n4 + 45n5 + 6n5 + n6)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 31594n2 + 42930n2 = 74524n2 n(332640 + 245004n + 74524n2 + 7155n3 + 4830n3 + 805n4 + 270n4 + 45n5 + 6n5 + n6)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 7155n3 + 4830n3 = 11985n3 n(332640 + 245004n + 74524n2 + 11985n3 + 805n4 + 270n4 + 45n5 + 6n5 + n6)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 805n4 + 270n4 = 1075n4 n(332640 + 245004n + 74524n2 + 11985n3 + 1075n4 + 45n5 + 6n5 + n6)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 45n5 + 6n5 = 51n5 n(332640 + 245004n + 74524n2 + 11985n3 + 1075n4 + 51n5 + n6)(5 + n)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Multiply (332640 + 245004n + 74524n2 + 11985n3 + 1075n4 + 51n5 + n6) * (5 + n) 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)(1 + n) = 0 n((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)(1 + n) = 0 n((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)(1 + n) = 0 n(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)(1 + n) = 0 n(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)(1 + n) = 0 n(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)(1 + n) = 0 n(1663200 + 332640n + 1225020n + 245004n2 + (372620n2 + 74524n3) + 11985n3 * (5 + n) + 1075n4 * (5 + n) + 51n5 * (5 + n) + n6(5 + n))(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(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)(1 + n) = 0 n(1663200 + 332640n + 1225020n + 245004n2 + 372620n2 + 74524n3 + (59925n3 + 11985n4) + 1075n4 * (5 + n) + 51n5 * (5 + n) + n6(5 + n))(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(1663200 + 332640n + 1225020n + 245004n2 + 372620n2 + 74524n3 + 59925n3 + 11985n4 + (5 * 1075n4 + n * 1075n4) + 51n5 * (5 + n) + n6(5 + n))(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(1663200 + 332640n + 1225020n + 245004n2 + 372620n2 + 74524n3 + 59925n3 + 11985n4 + (5375n4 + 1075n5) + 51n5 * (5 + n) + n6(5 + n))(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(1663200 + 332640n + 1225020n + 245004n2 + 372620n2 + 74524n3 + 59925n3 + 11985n4 + 5375n4 + 1075n5 + (5 * 51n5 + n * 51n5) + n6(5 + n))(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(1663200 + 332640n + 1225020n + 245004n2 + 372620n2 + 74524n3 + 59925n3 + 11985n4 + 5375n4 + 1075n5 + (255n5 + 51n6) + n6(5 + n))(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(1663200 + 332640n + 1225020n + 245004n2 + 372620n2 + 74524n3 + 59925n3 + 11985n4 + 5375n4 + 1075n5 + 255n5 + 51n6 + (5 * n6 + n * n6))(4 + n)(3 + n)(2 + n)(1 + n) = 0 n(1663200 + 332640n + 1225020n + 245004n2 + 372620n2 + 74524n3 + 59925n3 + 11985n4 + 5375n4 + 1075n5 + 255n5 + 51n6 + (5n6 + n7))(4 + n)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 332640n + 1225020n = 1557660n n(1663200 + 1557660n + 245004n2 + 372620n2 + 74524n3 + 59925n3 + 11985n4 + 5375n4 + 1075n5 + 255n5 + 51n6 + 5n6 + n7)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 245004n2 + 372620n2 = 617624n2 n(1663200 + 1557660n + 617624n2 + 74524n3 + 59925n3 + 11985n4 + 5375n4 + 1075n5 + 255n5 + 51n6 + 5n6 + n7)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 74524n3 + 59925n3 = 134449n3 n(1663200 + 1557660n + 617624n2 + 134449n3 + 11985n4 + 5375n4 + 1075n5 + 255n5 + 51n6 + 5n6 + n7)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 11985n4 + 5375n4 = 17360n4 n(1663200 + 1557660n + 617624n2 + 134449n3 + 17360n4 + 1075n5 + 255n5 + 51n6 + 5n6 + n7)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 1075n5 + 255n5 = 1330n5 n(1663200 + 1557660n + 617624n2 + 134449n3 + 17360n4 + 1330n5 + 51n6 + 5n6 + n7)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 51n6 + 5n6 = 56n6 n(1663200 + 1557660n + 617624n2 + 134449n3 + 17360n4 + 1330n5 + 56n6 + n7)(4 + n)(3 + n)(2 + n)(1 + n) = 0 Multiply (1663200 + 1557660n + 617624n2 + 134449n3 + 17360n4 + 1330n5 + 56n6 + n7) * (4 + n) 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)(1 + n) = 0 n((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)(1 + n) = 0 n((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)(1 + n) = 0 n(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)(1 + n) = 0 n(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)(1 + n) = 0 n(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)(1 + n) = 0 n(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)(1 + n) = 0 n(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)(1 + n) = 0 n(6652800 + 1663200n + 6230640n + 1557660n2 + 2470496n2 + 617624n3 + (537796n3 + 134449n4) + 17360n4 * (4 + n) + 1330n5 * (4 + n) + 56n6 * (4 + n) + n7(4 + n))(3 + n)(2 + n)(1 + n) = 0 n(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)(1 + n) = 0 n(6652800 + 1663200n + 6230640n + 1557660n2 + 2470496n2 + 617624n3 + 537796n3 + 134449n4 + (69440n4 + 17360n5) + 1330n5 * (4 + n) + 56n6 * (4 + n) + n7(4 + n))(3 + n)(2 + n)(1 + n) = 0 n(6652800 + 1663200n + 6230640n + 1557660n2 + 2470496n2 + 617624n3 + 537796n3 + 134449n4 + 69440n4 + 17360n5 + (4 * 1330n5 + n * 1330n5) + 56n6 * (4 + n) + n7(4 + n))(3 + n)(2 + n)(1 + n) = 0 n(6652800 + 1663200n + 6230640n + 1557660n2 + 2470496n2 + 617624n3 + 537796n3 + 134449n4 + 69440n4 + 17360n5 + (5320n5 + 1330n6) + 56n6 * (4 + n) + n7(4 + n))(3 + n)(2 + n)(1 + n) = 0 n(6652800 + 1663200n + 6230640n + 1557660n2 + 2470496n2 + 617624n3 + 537796n3 + 134449n4 + 69440n4 + 17360n5 + 5320n5 + 1330n6 + (4 * 56n6 + n * 56n6) + n7(4 + n))(3 + n)(2 + n)(1 + n) = 0 n(6652800 + 1663200n + 6230640n + 1557660n2 + 2470496n2 + 617624n3 + 537796n3 + 134449n4 + 69440n4 + 17360n5 + 5320n5 + 1330n6 + (224n6 + 56n7) + n7(4 + n))(3 + n)(2 + n)(1 + n) = 0 n(6652800 + 1663200n + 6230640n + 1557660n2 + 2470496n2 + 617624n3 + 537796n3 + 134449n4 + 69440n4 + 17360n5 + 5320n5 + 1330n6 + 224n6 + 56n7 + (4 * n7 + n * n7))(3 + n)(2 + n)(1 + n) = 0 n(6652800 + 1663200n + 6230640n + 1557660n2 + 2470496n2 + 617624n3 + 537796n3 + 134449n4 + 69440n4 + 17360n5 + 5320n5 + 1330n6 + 224n6 + 56n7 + (4n7 + n8))(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 1663200n + 6230640n = 7893840n n(6652800 + 7893840n + 1557660n2 + 2470496n2 + 617624n3 + 537796n3 + 134449n4 + 69440n4 + 17360n5 + 5320n5 + 1330n6 + 224n6 + 56n7 + 4n7 + n8)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 1557660n2 + 2470496n2 = 4028156n2 n(6652800 + 7893840n + 4028156n2 + 617624n3 + 537796n3 + 134449n4 + 69440n4 + 17360n5 + 5320n5 + 1330n6 + 224n6 + 56n7 + 4n7 + n8)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 617624n3 + 537796n3 = 1155420n3 n(6652800 + 7893840n + 4028156n2 + 1155420n3 + 134449n4 + 69440n4 + 17360n5 + 5320n5 + 1330n6 + 224n6 + 56n7 + 4n7 + n8)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 134449n4 + 69440n4 = 203889n4 n(6652800 + 7893840n + 4028156n2 + 1155420n3 + 203889n4 + 17360n5 + 5320n5 + 1330n6 + 224n6 + 56n7 + 4n7 + n8)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 17360n5 + 5320n5 = 22680n5 n(6652800 + 7893840n + 4028156n2 + 1155420n3 + 203889n4 + 22680n5 + 1330n6 + 224n6 + 56n7 + 4n7 + n8)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 1330n6 + 224n6 = 1554n6 n(6652800 + 7893840n + 4028156n2 + 1155420n3 + 203889n4 + 22680n5 + 1554n6 + 56n7 + 4n7 + n8)(3 + n)(2 + n)(1 + n) = 0 Combine like terms: 56n7 + 4n7 = 60n7 n(6652800 + 7893840n + 4028156n2 + 1155420n3 + 203889n4 + 22680n5 + 1554n6 + 60n7 + n8)(3 + n)(2 + n)(1 + n) = 0 Multiply (6652800 + 7893840n + 4028156n2 + 1155420n3 + 203889n4 + 22680n5 + 1554n6 + 60n7 + n8) * (3 + n) 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)(1 + n) = 0 n((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)(1 + n) = 0 n((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)(1 + n) = 0 n(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)(1 + n) = 0 n(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)(1 + n) = 0 n(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)(1 + n) = 0 n(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)(1 + n) = 0 n(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)(1 + n) = 0 n(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)(1 + n) = 0 n(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)(1 + n) = 0 n(19958400 + 6652800n + 23681520n + 7893840n2 + 12084468n2 + 4028156n3 + 3466260n3 + 1155420n4 + (611667n4 + 203889n5) + 22680n5 * (3 + n) + 1554n6 * (3 + n) + 60n7 * (3 + n) + n8(3 + n))(2 + n)(1 + n) = 0 n(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)(1 + n) = 0 n(19958400 + 6652800n + 23681520n + 7893840n2 + 12084468n2 + 4028156n3 + 3466260n3 + 1155420n4 + 611667n4 + 203889n5 + (68040n5 + 22680n6) + 1554n6 * (3 + n) + 60n7 * (3 + n) + n8(3 + n))(2 + n)(1 + n) = 0 n(19958400 + 6652800n + 23681520n + 7893840n2 + 12084468n2 + 4028156n3 + 3466260n3 + 1155420n4 + 611667n4 + 203889n5 + 68040n5 + 22680n6 + (3 * 1554n6 + n * 1554n6) + 60n7 * (3 + n) + n8(3 + n))(2 + n)(1 + n) = 0 n(19958400 + 6652800n + 23681520n + 7893840n2 + 12084468n2 + 4028156n3 + 3466260n3 + 1155420n4 + 611667n4 + 203889n5 + 68040n5 + 22680n6 + (4662n6 + 1554n7) + 60n7 * (3 + n) + n8(3 + n))(2 + n)(1 + n) = 0 n(19958400 + 6652800n + 23681520n + 7893840n2 + 12084468n2 + 4028156n3 + 3466260n3 + 1155420n4 + 611667n4 + 203889n5 + 68040n5 + 22680n6 + 4662n6 + 1554n7 + (3 * 60n7 + n * 60n7) + n8(3 + n))(2 + n)(1 + n) = 0 n(19958400 + 6652800n + 23681520n + 7893840n2 + 12084468n2 + 4028156n3 + 3466260n3 + 1155420n4 + 611667n4 + 203889n5 + 68040n5 + 22680n6 + 4662n6 + 1554n7 + (180n7 + 60n8) + n8(3 + n))(2 + n)(1 + n) = 0 n(19958400 + 6652800n + 23681520n + 7893840n2 + 12084468n2 + 4028156n3 + 3466260n3 + 1155420n4 + 611667n4 + 203889n5 + 68040n5 + 22680n6 + 4662n6 + 1554n7 + 180n7 + 60n8 + (3 * n8 + n * n8))(2 + n)(1 + n) = 0 n(19958400 + 6652800n + 23681520n + 7893840n2 + 12084468n2 + 4028156n3 + 3466260n3 + 1155420n4 + 611667n4 + 203889n5 + 68040n5 + 22680n6 + 4662n6 + 1554n7 + 180n7 + 60n8 + (3n8 + n9))(2 + n)(1 + n) = 0 Combine like terms: 6652800n + 23681520n = 30334320n n(19958400 + 30334320n + 7893840n2 + 12084468n2 + 4028156n3 + 3466260n3 + 1155420n4 + 611667n4 + 203889n5 + 68040n5 + 22680n6 + 4662n6 + 1554n7 + 180n7 + 60n8 + 3n8 + n9)(2 + n)(1 + n) = 0 Combine like terms: 7893840n2 + 12084468n2 = 19978308n2 n(19958400 + 30334320n + 19978308n2 + 4028156n3 + 3466260n3 + 1155420n4 + 611667n4 + 203889n5 + 68040n5 + 22680n6 + 4662n6 + 1554n7 + 180n7 + 60n8 + 3n8 + n9)(2 + n)(1 + n) = 0 Combine like terms: 4028156n3 + 3466260n3 = 7494416n3 n(19958400 + 30334320n + 19978308n2 + 7494416n3 + 1155420n4 + 611667n4 + 203889n5 + 68040n5 + 22680n6 + 4662n6 + 1554n7 + 180n7 + 60n8 + 3n8 + n9)(2 + n)(1 + n) = 0 Combine like terms: 1155420n4 + 611667n4 = 1767087n4 n(19958400 + 30334320n + 19978308n2 + 7494416n3 + 1767087n4 + 203889n5 + 68040n5 + 22680n6 + 4662n6 + 1554n7 + 180n7 + 60n8 + 3n8 + n9)(2 + n)(1 + n) = 0 Combine like terms: 203889n5 + 68040n5 = 271929n5 n(19958400 + 30334320n + 19978308n2 + 7494416n3 + 1767087n4 + 271929n5 + 22680n6 + 4662n6 + 1554n7 + 180n7 + 60n8 + 3n8 + n9)(2 + n)(1 + n) = 0 Combine like terms: 22680n6 + 4662n6 = 27342n6 n(19958400 + 30334320n + 19978308n2 + 7494416n3 + 1767087n4 + 271929n5 + 27342n6 + 1554n7 + 180n7 + 60n8 + 3n8 + n9)(2 + n)(1 + n) = 0 Combine like terms: 1554n7 + 180n7 = 1734n7 n(19958400 + 30334320n + 19978308n2 + 7494416n3 + 1767087n4 + 271929n5 + 27342n6 + 1734n7 + 60n8 + 3n8 + n9)(2 + n)(1 + n) = 0 Combine like terms: 60n8 + 3n8 = 63n8 n(19958400 + 30334320n + 19978308n2 + 7494416n3 + 1767087n4 + 271929n5 + 27342n6 + 1734n7 + 63n8 + n9)(2 + n)(1 + n) = 0 Multiply (19958400 + 30334320n + 19978308n2 + 7494416n3 + 1767087n4 + 271929n5 + 27342n6 + 1734n7 + 63n8 + n9) * (2 + n) 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))(1 + n) = 0 n((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))(1 + n) = 0 n((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))(1 + n) = 0 n(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))(1 + n) = 0 n(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))(1 + n) = 0 n(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))(1 + n) = 0 n(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))(1 + n) = 0 n(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))(1 + n) = 0 n(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))(1 + n) = 0 n(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))(1 + n) = 0 n(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))(1 + n) = 0 n(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))(1 + n) = 0 n(39916800 + 19958400n + 60668640n + 30334320n2 + 39956616n2 + 19978308n3 + 14988832n3 + 7494416n4 + 3534174n4 + 1767087n5 + (543858n5 + 271929n6) + 27342n6 * (2 + n) + 1734n7 * (2 + n) + 63n8 * (2 + n) + n9(2 + n))(1 + n) = 0 n(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))(1 + n) = 0 n(39916800 + 19958400n + 60668640n + 30334320n2 + 39956616n2 + 19978308n3 + 14988832n3 + 7494416n4 + 3534174n4 + 1767087n5 + 543858n5 + 271929n6 + (54684n6 + 27342n7) + 1734n7 * (2 + n) + 63n8 * (2 + n) + n9(2 + n))(1 + n) = 0 n(39916800 + 19958400n + 60668640n + 30334320n2 + 39956616n2 + 19978308n3 + 14988832n3 + 7494416n4 + 3534174n4 + 1767087n5 + 543858n5 + 271929n6 + 54684n6 + 27342n7 + (2 * 1734n7 + n * 1734n7) + 63n8 * (2 + n) + n9(2 + n))(1 + n) = 0 n(39916800 + 19958400n + 60668640n + 30334320n2 + 39956616n2 + 19978308n3 + 14988832n3 + 7494416n4 + 3534174n4 + 1767087n5 + 543858n5 + 271929n6 + 54684n6 + 27342n7 + (3468n7 + 1734n8) + 63n8 * (2 + n) + n9(2 + n))(1 + n) = 0 n(39916800 + 19958400n + 60668640n + 30334320n2 + 39956616n2 + 19978308n3 + 14988832n3 + 7494416n4 + 3534174n4 + 1767087n5 + 543858n5 + 271929n6 + 54684n6 + 27342n7 + 3468n7 + 1734n8 + (2 * 63n8 + n * 63n8) + n9(2 + n))(1 + n) = 0 n(39916800 + 19958400n + 60668640n + 30334320n2 + 39956616n2 + 19978308n3 + 14988832n3 + 7494416n4 + 3534174n4 + 1767087n5 + 543858n5 + 271929n6 + 54684n6 + 27342n7 + 3468n7 + 1734n8 + (126n8 + 63n9) + n9(2 + n))(1 + n) = 0 n(39916800 + 19958400n + 60668640n + 30334320n2 + 39956616n2 + 19978308n3 + 14988832n3 + 7494416n4 + 3534174n4 + 1767087n5 + 543858n5 + 271929n6 + 54684n6 + 27342n7 + 3468n7 + 1734n8 + 126n8 + 63n9 + (2 * n9 + n * n9))(1 + n) = 0 n(39916800 + 19958400n + 60668640n + 30334320n2 + 39956616n2 + 19978308n3 + 14988832n3 + 7494416n4 + 3534174n4 + 1767087n5 + 543858n5 + 271929n6 + 54684n6 + 27342n7 + 3468n7 + 1734n8 + 126n8 + 63n9 + (2n9 + n10))(1 + n) = 0 Combine like terms: 19958400n + 60668640n = 80627040n n(39916800 + 80627040n + 30334320n2 + 39956616n2 + 19978308n3 + 14988832n3 + 7494416n4 + 3534174n4 + 1767087n5 + 543858n5 + 271929n6 + 54684n6 + 27342n7 + 3468n7 + 1734n8 + 126n8 + 63n9 + 2n9 + n10)(1 + n) = 0 Combine like terms: 30334320n2 + 39956616n2 = 70290936n2 n(39916800 + 80627040n + 70290936n2 + 19978308n3 + 14988832n3 + 7494416n4 + 3534174n4 + 1767087n5 + 543858n5 + 271929n6 + 54684n6 + 27342n7 + 3468n7 + 1734n8 + 126n8 + 63n9 + 2n9 + n10)(1 + n) = 0 Combine like terms: 19978308n3 + 14988832n3 = 34967140n3 n(39916800 + 80627040n + 70290936n2 + 34967140n3 + 7494416n4 + 3534174n4 + 1767087n5 + 543858n5 + 271929n6 + 54684n6 + 27342n7 + 3468n7 + 1734n8 + 126n8 + 63n9 + 2n9 + n10)(1 + n) = 0 Combine like terms: 7494416n4 + 3534174n4 = 11028590n4 n(39916800 + 80627040n + 70290936n2 + 34967140n3 + 11028590n4 + 1767087n5 + 543858n5 + 271929n6 + 54684n6 + 27342n7 + 3468n7 + 1734n8 + 126n8 + 63n9 + 2n9 + n10)(1 + n) = 0 Combine like terms: 1767087n5 + 543858n5 = 2310945n5 n(39916800 + 80627040n + 70290936n2 + 34967140n3 + 11028590n4 + 2310945n5 + 271929n6 + 54684n6 + 27342n7 + 3468n7 + 1734n8 + 126n8 + 63n9 + 2n9 + n10)(1 + n) = 0 Combine like terms: 271929n6 + 54684n6 = 326613n6 n(39916800 + 80627040n + 70290936n2 + 34967140n3 + 11028590n4 + 2310945n5 + 326613n6 + 27342n7 + 3468n7 + 1734n8 + 126n8 + 63n9 + 2n9 + n10)(1 + n) = 0 Combine like terms: 27342n7 + 3468n7 = 30810n7 n(39916800 + 80627040n + 70290936n2 + 34967140n3 + 11028590n4 + 2310945n5 + 326613n6 + 30810n7 + 1734n8 + 126n8 + 63n9 + 2n9 + n10)(1 + n) = 0 Combine like terms: 1734n8 + 126n8 = 1860n8 n(39916800 + 80627040n + 70290936n2 + 34967140n3 + 11028590n4 + 2310945n5 + 326613n6 + 30810n7 + 1860n8 + 63n9 + 2n9 + n10)(1 + n) = 0 Combine like terms: 63n9 + 2n9 = 65n9 n(39916800 + 80627040n + 70290936n2 + 34967140n3 + 11028590n4 + 2310945n5 + 326613n6 + 30810n7 + 1860n8 + 65n9 + n10)(1 + n) = 0 Multiply (39916800 + 80627040n + 70290936n2 + 34967140n3 + 11028590n4 + 2310945n5 + 326613n6 + 30810n7 + 1860n8 + 65n9 + n10) * (1 + n) n(39916800(1 + n) + 80627040n * (1 + n) + 70290936n2 * (1 + n) + 34967140n3 * (1 + n) + 11028590n4 * (1 + n) + 2310945n5 * (1 + n) + 326613n6 * (1 + n) + 30810n7 * (1 + n) + 1860n8 * (1 + n) + 65n9 * (1 + n) + n10(1 + n)) = 0 n((1 * 39916800 + n * 39916800) + 80627040n * (1 + n) + 70290936n2 * (1 + n) + 34967140n3 * (1 + n) + 11028590n4 * (1 + n) + 2310945n5 * (1 + n) + 326613n6 * (1 + n) + 30810n7 * (1 + n) + 1860n8 * (1 + n) + 65n9 * (1 + n) + n10(1 + n)) = 0 n((39916800 + 39916800n) + 80627040n * (1 + n) + 70290936n2 * (1 + n) + 34967140n3 * (1 + n) + 11028590n4 * (1 + n) + 2310945n5 * (1 + n) + 326613n6 * (1 + n) + 30810n7 * (1 + n) + 1860n8 * (1 + n) + 65n9 * (1 + n) + n10(1 + n)) = 0 n(39916800 + 39916800n + (1 * 80627040n + n * 80627040n) + 70290936n2 * (1 + n) + 34967140n3 * (1 + n) + 11028590n4 * (1 + n) + 2310945n5 * (1 + n) + 326613n6 * (1 + n) + 30810n7 * (1 + n) + 1860n8 * (1 + n) + 65n9 * (1 + n) + n10(1 + n)) = 0 n(39916800 + 39916800n + (80627040n + 80627040n2) + 70290936n2 * (1 + n) + 34967140n3 * (1 + n) + 11028590n4 * (1 + n) + 2310945n5 * (1 + n) + 326613n6 * (1 + n) + 30810n7 * (1 + n) + 1860n8 * (1 + n) + 65n9 * (1 + n) + n10(1 + n)) = 0 n(39916800 + 39916800n + 80627040n + 80627040n2 + (1 * 70290936n2 + n * 70290936n2) + 34967140n3 * (1 + n) + 11028590n4 * (1 + n) + 2310945n5 * (1 + n) + 326613n6 * (1 + n) + 30810n7 * (1 + n) + 1860n8 * (1 + n) + 65n9 * (1 + n) + n10(1 + n)) = 0 n(39916800 + 39916800n + 80627040n + 80627040n2 + (70290936n2 + 70290936n3) + 34967140n3 * (1 + n) + 11028590n4 * (1 + n) + 2310945n5 * (1 + n) + 326613n6 * (1 + n) + 30810n7 * (1 + n) + 1860n8 * (1 + n) + 65n9 * (1 + n) + n10(1 + n)) = 0 n(39916800 + 39916800n + 80627040n + 80627040n2 + 70290936n2 + 70290936n3 + (1 * 34967140n3 + n * 34967140n3) + 11028590n4 * (1 + n) + 2310945n5 * (1 + n) + 326613n6 * (1 + n) + 30810n7 * (1 + n) + 1860n8 * (1 + n) + 65n9 * (1 + n) + n10(1 + n)) = 0 n(39916800 + 39916800n + 80627040n + 80627040n2 + 70290936n2 + 70290936n3 + (34967140n3 + 34967140n4) + 11028590n4 * (1 + n) + 2310945n5 * (1 + n) + 326613n6 * (1 + n) + 30810n7 * (1 + n) + 1860n8 * (1 + n) + 65n9 * (1 + n) + n10(1 + n)) = 0 n(39916800 + 39916800n + 80627040n + 80627040n2 + 70290936n2 + 70290936n3 + 34967140n3 + 34967140n4 + (1 * 11028590n4 + n * 11028590n4) + 2310945n5 * (1 + n) + 326613n6 * (1 + n) + 30810n7 * (1 + n) + 1860n8 * (1 + n) + 65n9 * (1 + n) + n10(1 + n)) = 0 n(39916800 + 39916800n + 80627040n + 80627040n2 + 70290936n2 + 70290936n3 + 34967140n3 + 34967140n4 + (11028590n4 + 11028590n5) + 2310945n5 * (1 + n) + 326613n6 * (1 + n) + 30810n7 * (1 + n) + 1860n8 * (1 + n) + 65n9 * (1 + n) + n10(1 + n)) = 0 n(39916800 + 39916800n + 80627040n + 80627040n2 + 70290936n2 + 70290936n3 + 34967140n3 + 34967140n4 + 11028590n4 + 11028590n5 + (1 * 2310945n5 + n * 2310945n5) + 326613n6 * (1 + n) + 30810n7 * (1 + n) + 1860n8 * (1 + n) + 65n9 * (1 + n) + n10(1 + n)) = 0 n(39916800 + 39916800n + 80627040n + 80627040n2 + 70290936n2 + 70290936n3 + 34967140n3 + 34967140n4 + 11028590n4 + 11028590n5 + (2310945n5 + 2310945n6) + 326613n6 * (1 + n) + 30810n7 * (1 + n) + 1860n8 * (1 + n) + 65n9 * (1 + n) + n10(1 + n)) = 0 n(39916800 + 39916800n + 80627040n + 80627040n2 + 70290936n2 + 70290936n3 + 34967140n3 + 34967140n4 + 11028590n4 + 11028590n5 + 2310945n5 + 2310945n6 + (1 * 326613n6 + n * 326613n6) + 30810n7 * (1 + n) + 1860n8 * (1 + n) + 65n9 * (1 + n) + n10(1 + n)) = 0 n(39916800 + 39916800n + 80627040n + 80627040n2 + 70290936n2 + 70290936n3 + 34967140n3 + 34967140n4 + 11028590n4 + 11028590n5 + 2310945n5 + 2310945n6 + (326613n6 + 326613n7) + 30810n7 * (1 + n) + 1860n8 * (1 + n) + 65n9 * (1 + n) + n10(1 + n)) = 0 n(39916800 + 39916800n + 80627040n + 80627040n2 + 70290936n2 + 70290936n3 + 34967140n3 + 34967140n4 + 11028590n4 + 11028590n5 + 2310945n5 + 2310945n6 + 326613n6 + 326613n7 + (1 * 30810n7 + n * 30810n7) + 1860n8 * (1 + n) + 65n9 * (1 + n) + n10(1 + n)) = 0 n(39916800 + 39916800n + 80627040n + 80627040n2 + 70290936n2 + 70290936n3 + 34967140n3 + 34967140n4 + 11028590n4 + 11028590n5 + 2310945n5 + 2310945n6 + 326613n6 + 326613n7 + (30810n7 + 30810n8) + 1860n8 * (1 + n) + 65n9 * (1 + n) + n10(1 + n)) = 0 n(39916800 + 39916800n + 80627040n + 80627040n2 + 70290936n2 + 70290936n3 + 34967140n3 + 34967140n4 + 11028590n4 + 11028590n5 + 2310945n5 + 2310945n6 + 326613n6 + 326613n7 + 30810n7 + 30810n8 + (1 * 1860n8 + n * 1860n8) + 65n9 * (1 + n) + n10(1 + n)) = 0 n(39916800 + 39916800n + 80627040n + 80627040n2 + 70290936n2 + 70290936n3 + 34967140n3 + 34967140n4 + 11028590n4 + 11028590n5 + 2310945n5 + 2310945n6 + 326613n6 + 326613n7 + 30810n7 + 30810n8 + (1860n8 + 1860n9) + 65n9 * (1 + n) + n10(1 + n)) = 0 n(39916800 + 39916800n + 80627040n + 80627040n2 + 70290936n2 + 70290936n3 + 34967140n3 + 34967140n4 + 11028590n4 + 11028590n5 + 2310945n5 + 2310945n6 + 326613n6 + 326613n7 + 30810n7 + 30810n8 + 1860n8 + 1860n9 + (1 * 65n9 + n * 65n9) + n10(1 + n)) = 0 n(39916800 + 39916800n + 80627040n + 80627040n2 + 70290936n2 + 70290936n3 + 34967140n3 + 34967140n4 + 11028590n4 + 11028590n5 + 2310945n5 + 2310945n6 + 326613n6 + 326613n7 + 30810n7 + 30810n8 + 1860n8 + 1860n9 + (65n9 + 65n10) + n10(1 + n)) = 0 n(39916800 + 39916800n + 80627040n + 80627040n2 + 70290936n2 + 70290936n3 + 34967140n3 + 34967140n4 + 11028590n4 + 11028590n5 + 2310945n5 + 2310945n6 + 326613n6 + 326613n7 + 30810n7 + 30810n8 + 1860n8 + 1860n9 + 65n9 + 65n10 + (1 * n10 + n * n10)) = 0 n(39916800 + 39916800n + 80627040n + 80627040n2 + 70290936n2 + 70290936n3 + 34967140n3 + 34967140n4 + 11028590n4 + 11028590n5 + 2310945n5 + 2310945n6 + 326613n6 + 326613n7 + 30810n7 + 30810n8 + 1860n8 + 1860n9 + 65n9 + 65n10 + (1n10 + n11)) = 0 Combine like terms: 39916800n + 80627040n = 120543840n n(39916800 + 120543840n + 80627040n2 + 70290936n2 + 70290936n3 + 34967140n3 + 34967140n4 + 11028590n4 + 11028590n5 + 2310945n5 + 2310945n6 + 326613n6 + 326613n7 + 30810n7 + 30810n8 + 1860n8 + 1860n9 + 65n9 + 65n10 + 1n10 + n11) = 0 Combine like terms: 80627040n2 + 70290936n2 = 150917976n2 n(39916800 + 120543840n + 150917976n2 + 70290936n3 + 34967140n3 + 34967140n4 + 11028590n4 + 11028590n5 + 2310945n5 + 2310945n6 + 326613n6 + 326613n7 + 30810n7 + 30810n8 + 1860n8 + 1860n9 + 65n9 + 65n10 + 1n10 + n11) = 0 Combine like terms: 70290936n3 + 34967140n3 = 105258076n3 n(39916800 + 120543840n + 150917976n2 + 105258076n3 + 34967140n4 + 11028590n4 + 11028590n5 + 2310945n5 + 2310945n6 + 326613n6 + 326613n7 + 30810n7 + 30810n8 + 1860n8 + 1860n9 + 65n9 + 65n10 + 1n10 + n11) = 0 Combine like terms: 34967140n4 + 11028590n4 = 45995730n4 n(39916800 + 120543840n + 150917976n2 + 105258076n3 + 45995730n4 + 11028590n5 + 2310945n5 + 2310945n6 + 326613n6 + 326613n7 + 30810n7 + 30810n8 + 1860n8 + 1860n9 + 65n9 + 65n10 + 1n10 + n11) = 0 Combine like terms: 11028590n5 + 2310945n5 = 13339535n5 n(39916800 + 120543840n + 150917976n2 + 105258076n3 + 45995730n4 + 13339535n5 + 2310945n6 + 326613n6 + 326613n7 + 30810n7 + 30810n8 + 1860n8 + 1860n9 + 65n9 + 65n10 + 1n10 + n11) = 0 Combine like terms: 2310945n6 + 326613n6 = 2637558n6 n(39916800 + 120543840n + 150917976n2 + 105258076n3 + 45995730n4 + 13339535n5 + 2637558n6 + 326613n7 + 30810n7 + 30810n8 + 1860n8 + 1860n9 + 65n9 + 65n10 + 1n10 + n11) = 0 Combine like terms: 326613n7 + 30810n7 = 357423n7 n(39916800 + 120543840n + 150917976n2 + 105258076n3 + 45995730n4 + 13339535n5 + 2637558n6 + 357423n7 + 30810n8 + 1860n8 + 1860n9 + 65n9 + 65n10 + 1n10 + n11) = 0 Combine like terms: 30810n8 + 1860n8 = 32670n8 n(39916800 + 120543840n + 150917976n2 + 105258076n3 + 45995730n4 + 13339535n5 + 2637558n6 + 357423n7 + 32670n8 + 1860n9 + 65n9 + 65n10 + 1n10 + n11) = 0 Combine like terms: 1860n9 + 65n9 = 1925n9 n(39916800 + 120543840n + 150917976n2 + 105258076n3 + 45995730n4 + 13339535n5 + 2637558n6 + 357423n7 + 32670n8 + 1925n9 + 65n10 + 1n10 + n11) = 0 Combine like terms: 65n10 + 1n10 = 66n10 n(39916800 + 120543840n + 150917976n2 + 105258076n3 + 45995730n4 + 13339535n5 + 2637558n6 + 357423n7 + 32670n8 + 1925n9 + 66n10 + n11) = 0 (39916800 * n + 120543840n * n + 150917976n2 * n + 105258076n3 * n + 45995730n4 * n + 13339535n5 * n + 2637558n6 * n + 357423n7 * n + 32670n8 * n + 1925n9 * n + 66n10 * n + n11 * n) = 0 (39916800n + 120543840n2 + 150917976n3 + 105258076n4 + 45995730n5 + 13339535n6 + 2637558n7 + 357423n8 + 32670n9 + 1925n10 + 66n11 + n12) = 0 Solving 39916800n + 120543840n2 + 150917976n3 + 105258076n4 + 45995730n5 + 13339535n6 + 2637558n7 + 357423n8 + 32670n9 + 1925n10 + 66n11 + n12 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(39916800 + 120543840n + 150917976n2 + 105258076n3 + 45995730n4 + 13339535n5 + 2637558n6 + 357423n7 + 32670n8 + 1925n9 + 66n10 + n11) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(39916800 + 120543840n + 150917976n2 + 105258076n3 + 45995730n4 + 13339535n5 + 2637558n6 + 357423n7 + 32670n8 + 1925n9 + 66n10 + n11)' equal to zero and attempt to solve: Simplifying 39916800 + 120543840n + 150917976n2 + 105258076n3 + 45995730n4 + 13339535n5 + 2637558n6 + 357423n7 + 32670n8 + 1925n9 + 66n10 + n11 = 0 Solving 39916800 + 120543840n + 150917976n2 + 105258076n3 + 45995730n4 + 13339535n5 + 2637558n6 + 357423n7 + 32670n8 + 1925n9 + 66n10 + n11 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
n = {0}
| 28-9=19 | | 29=5(8)+b | | -11+15=4 | | 4x-9+x=-3+31 | | 5ln(x)=40 | | y-8x=35 | | .14(x+7)=.07(2x+14) | | 6v-10=-(-6+10) | | 4x-1y=-8 | | 14=5(3)+b | | -8x+y=35 | | 18x-3+39=27x | | -1-(-3y-3)=-5(7y+6)+6 | | 7(5r+3)=-154 | | 3x+3x+5+5= | | 38=13+5v | | A=2xy+2xz+2yz | | 3+5x=8x | | -4u^2-u+u^2+2u^2= | | 2x^2+18x-30=0 | | -3x^2+2x+40=0 | | x((0.2x^2)+1)-400=0 | | 2x+(3x-1)-3=8x-2x+4 | | 4d-8=58 | | 6x+10+76=2+13x | | 5c^2+c-4c^2-c= | | 10x^4+3x^2=0 | | -1+8(x-3)=16x+6-8x | | (-2x-9)(-4)= | | 2x^2-16x= | | .2(x+3)=4x-5(2-x)-7 | | 2(x+9)=3(x-8) |