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Simplifying (8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(n + -1)(n + -2)(n + -3) = 0 Reorder the terms: (8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(n + -2)(n + -3) = 0 Reorder the terms: (8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(n + -3) = 0 Reorder the terms: (8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Multiply (8 + n) * (7 + n) (8(7 + n) + n(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((7 * 8 + n * 8) + n(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((56 + 8n) + n(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (56 + 8n + (7 * n + n * n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (56 + 8n + (7n + n2))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 8n + 7n = 15n (56 + 15n + n2)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Multiply (56 + 15n + n2) * (6 + n) (56(6 + n) + 15n * (6 + n) + n2(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((6 * 56 + n * 56) + 15n * (6 + n) + n2(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((336 + 56n) + 15n * (6 + n) + n2(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (336 + 56n + (6 * 15n + n * 15n) + n2(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (336 + 56n + (90n + 15n2) + n2(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (336 + 56n + 90n + 15n2 + (6 * n2 + n * n2))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (336 + 56n + 90n + 15n2 + (6n2 + n3))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 56n + 90n = 146n (336 + 146n + 15n2 + 6n2 + n3)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 15n2 + 6n2 = 21n2 (336 + 146n + 21n2 + n3)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Multiply (336 + 146n + 21n2 + n3) * (5 + n) (336(5 + n) + 146n * (5 + n) + 21n2 * (5 + n) + n3(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((5 * 336 + n * 336) + 146n * (5 + n) + 21n2 * (5 + n) + n3(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((1680 + 336n) + 146n * (5 + n) + 21n2 * (5 + n) + n3(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (1680 + 336n + (5 * 146n + n * 146n) + 21n2 * (5 + n) + n3(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (1680 + 336n + (730n + 146n2) + 21n2 * (5 + n) + n3(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (1680 + 336n + 730n + 146n2 + (5 * 21n2 + n * 21n2) + n3(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (1680 + 336n + 730n + 146n2 + (105n2 + 21n3) + n3(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (1680 + 336n + 730n + 146n2 + 105n2 + 21n3 + (5 * n3 + n * n3))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (1680 + 336n + 730n + 146n2 + 105n2 + 21n3 + (5n3 + n4))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 336n + 730n = 1066n (1680 + 1066n + 146n2 + 105n2 + 21n3 + 5n3 + n4)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 146n2 + 105n2 = 251n2 (1680 + 1066n + 251n2 + 21n3 + 5n3 + n4)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 21n3 + 5n3 = 26n3 (1680 + 1066n + 251n2 + 26n3 + n4)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Multiply (1680 + 1066n + 251n2 + 26n3 + n4) * (4 + n) (1680(4 + n) + 1066n * (4 + n) + 251n2 * (4 + n) + 26n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((4 * 1680 + n * 1680) + 1066n * (4 + n) + 251n2 * (4 + n) + 26n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((6720 + 1680n) + 1066n * (4 + n) + 251n2 * (4 + n) + 26n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (6720 + 1680n + (4 * 1066n + n * 1066n) + 251n2 * (4 + n) + 26n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (6720 + 1680n + (4264n + 1066n2) + 251n2 * (4 + n) + 26n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (6720 + 1680n + 4264n + 1066n2 + (4 * 251n2 + n * 251n2) + 26n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (6720 + 1680n + 4264n + 1066n2 + (1004n2 + 251n3) + 26n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (6720 + 1680n + 4264n + 1066n2 + 1004n2 + 251n3 + (4 * 26n3 + n * 26n3) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (6720 + 1680n + 4264n + 1066n2 + 1004n2 + 251n3 + (104n3 + 26n4) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (6720 + 1680n + 4264n + 1066n2 + 1004n2 + 251n3 + 104n3 + 26n4 + (4 * n4 + n * n4))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (6720 + 1680n + 4264n + 1066n2 + 1004n2 + 251n3 + 104n3 + 26n4 + (4n4 + n5))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 1680n + 4264n = 5944n (6720 + 5944n + 1066n2 + 1004n2 + 251n3 + 104n3 + 26n4 + 4n4 + n5)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 1066n2 + 1004n2 = 2070n2 (6720 + 5944n + 2070n2 + 251n3 + 104n3 + 26n4 + 4n4 + n5)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 251n3 + 104n3 = 355n3 (6720 + 5944n + 2070n2 + 355n3 + 26n4 + 4n4 + n5)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 26n4 + 4n4 = 30n4 (6720 + 5944n + 2070n2 + 355n3 + 30n4 + n5)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Multiply (6720 + 5944n + 2070n2 + 355n3 + 30n4 + n5) * (3 + n) (6720(3 + n) + 5944n * (3 + n) + 2070n2 * (3 + n) + 355n3 * (3 + n) + 30n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((3 * 6720 + n * 6720) + 5944n * (3 + n) + 2070n2 * (3 + n) + 355n3 * (3 + n) + 30n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((20160 + 6720n) + 5944n * (3 + n) + 2070n2 * (3 + n) + 355n3 * (3 + n) + 30n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (20160 + 6720n + (3 * 5944n + n * 5944n) + 2070n2 * (3 + n) + 355n3 * (3 + n) + 30n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (20160 + 6720n + (17832n + 5944n2) + 2070n2 * (3 + n) + 355n3 * (3 + n) + 30n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (20160 + 6720n + 17832n + 5944n2 + (3 * 2070n2 + n * 2070n2) + 355n3 * (3 + n) + 30n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (20160 + 6720n + 17832n + 5944n2 + (6210n2 + 2070n3) + 355n3 * (3 + n) + 30n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (20160 + 6720n + 17832n + 5944n2 + 6210n2 + 2070n3 + (3 * 355n3 + n * 355n3) + 30n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (20160 + 6720n + 17832n + 5944n2 + 6210n2 + 2070n3 + (1065n3 + 355n4) + 30n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (20160 + 6720n + 17832n + 5944n2 + 6210n2 + 2070n3 + 1065n3 + 355n4 + (3 * 30n4 + n * 30n4) + n5(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (20160 + 6720n + 17832n + 5944n2 + 6210n2 + 2070n3 + 1065n3 + 355n4 + (90n4 + 30n5) + n5(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (20160 + 6720n + 17832n + 5944n2 + 6210n2 + 2070n3 + 1065n3 + 355n4 + 90n4 + 30n5 + (3 * n5 + n * n5))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (20160 + 6720n + 17832n + 5944n2 + 6210n2 + 2070n3 + 1065n3 + 355n4 + 90n4 + 30n5 + (3n5 + n6))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 6720n + 17832n = 24552n (20160 + 24552n + 5944n2 + 6210n2 + 2070n3 + 1065n3 + 355n4 + 90n4 + 30n5 + 3n5 + n6)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 5944n2 + 6210n2 = 12154n2 (20160 + 24552n + 12154n2 + 2070n3 + 1065n3 + 355n4 + 90n4 + 30n5 + 3n5 + n6)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 2070n3 + 1065n3 = 3135n3 (20160 + 24552n + 12154n2 + 3135n3 + 355n4 + 90n4 + 30n5 + 3n5 + n6)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 355n4 + 90n4 = 445n4 (20160 + 24552n + 12154n2 + 3135n3 + 445n4 + 30n5 + 3n5 + n6)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 30n5 + 3n5 = 33n5 (20160 + 24552n + 12154n2 + 3135n3 + 445n4 + 33n5 + n6)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Multiply (20160 + 24552n + 12154n2 + 3135n3 + 445n4 + 33n5 + n6) * (2 + n) (20160(2 + n) + 24552n * (2 + n) + 12154n2 * (2 + n) + 3135n3 * (2 + n) + 445n4 * (2 + n) + 33n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 ((2 * 20160 + n * 20160) + 24552n * (2 + n) + 12154n2 * (2 + n) + 3135n3 * (2 + n) + 445n4 * (2 + n) + 33n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 ((40320 + 20160n) + 24552n * (2 + n) + 12154n2 * (2 + n) + 3135n3 * (2 + n) + 445n4 * (2 + n) + 33n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (40320 + 20160n + (2 * 24552n + n * 24552n) + 12154n2 * (2 + n) + 3135n3 * (2 + n) + 445n4 * (2 + n) + 33n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (40320 + 20160n + (49104n + 24552n2) + 12154n2 * (2 + n) + 3135n3 * (2 + n) + 445n4 * (2 + n) + 33n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (40320 + 20160n + 49104n + 24552n2 + (2 * 12154n2 + n * 12154n2) + 3135n3 * (2 + n) + 445n4 * (2 + n) + 33n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (40320 + 20160n + 49104n + 24552n2 + (24308n2 + 12154n3) + 3135n3 * (2 + n) + 445n4 * (2 + n) + 33n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (40320 + 20160n + 49104n + 24552n2 + 24308n2 + 12154n3 + (2 * 3135n3 + n * 3135n3) + 445n4 * (2 + n) + 33n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (40320 + 20160n + 49104n + 24552n2 + 24308n2 + 12154n3 + (6270n3 + 3135n4) + 445n4 * (2 + n) + 33n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (40320 + 20160n + 49104n + 24552n2 + 24308n2 + 12154n3 + 6270n3 + 3135n4 + (2 * 445n4 + n * 445n4) + 33n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (40320 + 20160n + 49104n + 24552n2 + 24308n2 + 12154n3 + 6270n3 + 3135n4 + (890n4 + 445n5) + 33n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (40320 + 20160n + 49104n + 24552n2 + 24308n2 + 12154n3 + 6270n3 + 3135n4 + 890n4 + 445n5 + (2 * 33n5 + n * 33n5) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (40320 + 20160n + 49104n + 24552n2 + 24308n2 + 12154n3 + 6270n3 + 3135n4 + 890n4 + 445n5 + (66n5 + 33n6) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (40320 + 20160n + 49104n + 24552n2 + 24308n2 + 12154n3 + 6270n3 + 3135n4 + 890n4 + 445n5 + 66n5 + 33n6 + (2 * n6 + n * n6))(-1 + n)(-2 + n)(-3 + n) = 0 (40320 + 20160n + 49104n + 24552n2 + 24308n2 + 12154n3 + 6270n3 + 3135n4 + 890n4 + 445n5 + 66n5 + 33n6 + (2n6 + n7))(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 20160n + 49104n = 69264n (40320 + 69264n + 24552n2 + 24308n2 + 12154n3 + 6270n3 + 3135n4 + 890n4 + 445n5 + 66n5 + 33n6 + 2n6 + n7)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 24552n2 + 24308n2 = 48860n2 (40320 + 69264n + 48860n2 + 12154n3 + 6270n3 + 3135n4 + 890n4 + 445n5 + 66n5 + 33n6 + 2n6 + n7)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 12154n3 + 6270n3 = 18424n3 (40320 + 69264n + 48860n2 + 18424n3 + 3135n4 + 890n4 + 445n5 + 66n5 + 33n6 + 2n6 + n7)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 3135n4 + 890n4 = 4025n4 (40320 + 69264n + 48860n2 + 18424n3 + 4025n4 + 445n5 + 66n5 + 33n6 + 2n6 + n7)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 445n5 + 66n5 = 511n5 (40320 + 69264n + 48860n2 + 18424n3 + 4025n4 + 511n5 + 33n6 + 2n6 + n7)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 33n6 + 2n6 = 35n6 (40320 + 69264n + 48860n2 + 18424n3 + 4025n4 + 511n5 + 35n6 + n7)(-1 + n)(-2 + n)(-3 + n) = 0 Multiply (40320 + 69264n + 48860n2 + 18424n3 + 4025n4 + 511n5 + 35n6 + n7) * (-1 + n) (40320(-1 + n) + 69264n * (-1 + n) + 48860n2 * (-1 + n) + 18424n3 * (-1 + n) + 4025n4 * (-1 + n) + 511n5 * (-1 + n) + 35n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 ((-1 * 40320 + n * 40320) + 69264n * (-1 + n) + 48860n2 * (-1 + n) + 18424n3 * (-1 + n) + 4025n4 * (-1 + n) + 511n5 * (-1 + n) + 35n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 ((-40320 + 40320n) + 69264n * (-1 + n) + 48860n2 * (-1 + n) + 18424n3 * (-1 + n) + 4025n4 * (-1 + n) + 511n5 * (-1 + n) + 35n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-40320 + 40320n + (-1 * 69264n + n * 69264n) + 48860n2 * (-1 + n) + 18424n3 * (-1 + n) + 4025n4 * (-1 + n) + 511n5 * (-1 + n) + 35n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-40320 + 40320n + (-69264n + 69264n2) + 48860n2 * (-1 + n) + 18424n3 * (-1 + n) + 4025n4 * (-1 + n) + 511n5 * (-1 + n) + 35n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-40320 + 40320n + -69264n + 69264n2 + (-1 * 48860n2 + n * 48860n2) + 18424n3 * (-1 + n) + 4025n4 * (-1 + n) + 511n5 * (-1 + n) + 35n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-40320 + 40320n + -69264n + 69264n2 + (-48860n2 + 48860n3) + 18424n3 * (-1 + n) + 4025n4 * (-1 + n) + 511n5 * (-1 + n) + 35n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-40320 + 40320n + -69264n + 69264n2 + -48860n2 + 48860n3 + (-1 * 18424n3 + n * 18424n3) + 4025n4 * (-1 + n) + 511n5 * (-1 + n) + 35n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-40320 + 40320n + -69264n + 69264n2 + -48860n2 + 48860n3 + (-18424n3 + 18424n4) + 4025n4 * (-1 + n) + 511n5 * (-1 + n) + 35n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-40320 + 40320n + -69264n + 69264n2 + -48860n2 + 48860n3 + -18424n3 + 18424n4 + (-1 * 4025n4 + n * 4025n4) + 511n5 * (-1 + n) + 35n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-40320 + 40320n + -69264n + 69264n2 + -48860n2 + 48860n3 + -18424n3 + 18424n4 + (-4025n4 + 4025n5) + 511n5 * (-1 + n) + 35n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-40320 + 40320n + -69264n + 69264n2 + -48860n2 + 48860n3 + -18424n3 + 18424n4 + -4025n4 + 4025n5 + (-1 * 511n5 + n * 511n5) + 35n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-40320 + 40320n + -69264n + 69264n2 + -48860n2 + 48860n3 + -18424n3 + 18424n4 + -4025n4 + 4025n5 + (-511n5 + 511n6) + 35n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-40320 + 40320n + -69264n + 69264n2 + -48860n2 + 48860n3 + -18424n3 + 18424n4 + -4025n4 + 4025n5 + -511n5 + 511n6 + (-1 * 35n6 + n * 35n6) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-40320 + 40320n + -69264n + 69264n2 + -48860n2 + 48860n3 + -18424n3 + 18424n4 + -4025n4 + 4025n5 + -511n5 + 511n6 + (-35n6 + 35n7) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-40320 + 40320n + -69264n + 69264n2 + -48860n2 + 48860n3 + -18424n3 + 18424n4 + -4025n4 + 4025n5 + -511n5 + 511n6 + -35n6 + 35n7 + (-1 * n7 + n * n7))(-2 + n)(-3 + n) = 0 (-40320 + 40320n + -69264n + 69264n2 + -48860n2 + 48860n3 + -18424n3 + 18424n4 + -4025n4 + 4025n5 + -511n5 + 511n6 + -35n6 + 35n7 + (-1n7 + n8))(-2 + n)(-3 + n) = 0 Combine like terms: 40320n + -69264n = -28944n (-40320 + -28944n + 69264n2 + -48860n2 + 48860n3 + -18424n3 + 18424n4 + -4025n4 + 4025n5 + -511n5 + 511n6 + -35n6 + 35n7 + -1n7 + n8)(-2 + n)(-3 + n) = 0 Combine like terms: 69264n2 + -48860n2 = 20404n2 (-40320 + -28944n + 20404n2 + 48860n3 + -18424n3 + 18424n4 + -4025n4 + 4025n5 + -511n5 + 511n6 + -35n6 + 35n7 + -1n7 + n8)(-2 + n)(-3 + n) = 0 Combine like terms: 48860n3 + -18424n3 = 30436n3 (-40320 + -28944n + 20404n2 + 30436n3 + 18424n4 + -4025n4 + 4025n5 + -511n5 + 511n6 + -35n6 + 35n7 + -1n7 + n8)(-2 + n)(-3 + n) = 0 Combine like terms: 18424n4 + -4025n4 = 14399n4 (-40320 + -28944n + 20404n2 + 30436n3 + 14399n4 + 4025n5 + -511n5 + 511n6 + -35n6 + 35n7 + -1n7 + n8)(-2 + n)(-3 + n) = 0 Combine like terms: 4025n5 + -511n5 = 3514n5 (-40320 + -28944n + 20404n2 + 30436n3 + 14399n4 + 3514n5 + 511n6 + -35n6 + 35n7 + -1n7 + n8)(-2 + n)(-3 + n) = 0 Combine like terms: 511n6 + -35n6 = 476n6 (-40320 + -28944n + 20404n2 + 30436n3 + 14399n4 + 3514n5 + 476n6 + 35n7 + -1n7 + n8)(-2 + n)(-3 + n) = 0 Combine like terms: 35n7 + -1n7 = 34n7 (-40320 + -28944n + 20404n2 + 30436n3 + 14399n4 + 3514n5 + 476n6 + 34n7 + n8)(-2 + n)(-3 + n) = 0 Multiply (-40320 + -28944n + 20404n2 + 30436n3 + 14399n4 + 3514n5 + 476n6 + 34n7 + n8) * (-2 + n) (-40320(-2 + n) + -28944n * (-2 + n) + 20404n2 * (-2 + n) + 30436n3 * (-2 + n) + 14399n4 * (-2 + n) + 3514n5 * (-2 + n) + 476n6 * (-2 + n) + 34n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 ((-2 * -40320 + n * -40320) + -28944n * (-2 + n) + 20404n2 * (-2 + n) + 30436n3 * (-2 + n) + 14399n4 * (-2 + n) + 3514n5 * (-2 + n) + 476n6 * (-2 + n) + 34n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 ((80640 + -40320n) + -28944n * (-2 + n) + 20404n2 * (-2 + n) + 30436n3 * (-2 + n) + 14399n4 * (-2 + n) + 3514n5 * (-2 + n) + 476n6 * (-2 + n) + 34n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (80640 + -40320n + (-2 * -28944n + n * -28944n) + 20404n2 * (-2 + n) + 30436n3 * (-2 + n) + 14399n4 * (-2 + n) + 3514n5 * (-2 + n) + 476n6 * (-2 + n) + 34n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (80640 + -40320n + (57888n + -28944n2) + 20404n2 * (-2 + n) + 30436n3 * (-2 + n) + 14399n4 * (-2 + n) + 3514n5 * (-2 + n) + 476n6 * (-2 + n) + 34n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (80640 + -40320n + 57888n + -28944n2 + (-2 * 20404n2 + n * 20404n2) + 30436n3 * (-2 + n) + 14399n4 * (-2 + n) + 3514n5 * (-2 + n) + 476n6 * (-2 + n) + 34n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (80640 + -40320n + 57888n + -28944n2 + (-40808n2 + 20404n3) + 30436n3 * (-2 + n) + 14399n4 * (-2 + n) + 3514n5 * (-2 + n) + 476n6 * (-2 + n) + 34n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (80640 + -40320n + 57888n + -28944n2 + -40808n2 + 20404n3 + (-2 * 30436n3 + n * 30436n3) + 14399n4 * (-2 + n) + 3514n5 * (-2 + n) + 476n6 * (-2 + n) + 34n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (80640 + -40320n + 57888n + -28944n2 + -40808n2 + 20404n3 + (-60872n3 + 30436n4) + 14399n4 * (-2 + n) + 3514n5 * (-2 + n) + 476n6 * (-2 + n) + 34n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (80640 + -40320n + 57888n + -28944n2 + -40808n2 + 20404n3 + -60872n3 + 30436n4 + (-2 * 14399n4 + n * 14399n4) + 3514n5 * (-2 + n) + 476n6 * (-2 + n) + 34n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (80640 + -40320n + 57888n + -28944n2 + -40808n2 + 20404n3 + -60872n3 + 30436n4 + (-28798n4 + 14399n5) + 3514n5 * (-2 + n) + 476n6 * (-2 + n) + 34n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (80640 + -40320n + 57888n + -28944n2 + -40808n2 + 20404n3 + -60872n3 + 30436n4 + -28798n4 + 14399n5 + (-2 * 3514n5 + n * 3514n5) + 476n6 * (-2 + n) + 34n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (80640 + -40320n + 57888n + -28944n2 + -40808n2 + 20404n3 + -60872n3 + 30436n4 + -28798n4 + 14399n5 + (-7028n5 + 3514n6) + 476n6 * (-2 + n) + 34n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (80640 + -40320n + 57888n + -28944n2 + -40808n2 + 20404n3 + -60872n3 + 30436n4 + -28798n4 + 14399n5 + -7028n5 + 3514n6 + (-2 * 476n6 + n * 476n6) + 34n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (80640 + -40320n + 57888n + -28944n2 + -40808n2 + 20404n3 + -60872n3 + 30436n4 + -28798n4 + 14399n5 + -7028n5 + 3514n6 + (-952n6 + 476n7) + 34n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (80640 + -40320n + 57888n + -28944n2 + -40808n2 + 20404n3 + -60872n3 + 30436n4 + -28798n4 + 14399n5 + -7028n5 + 3514n6 + -952n6 + 476n7 + (-2 * 34n7 + n * 34n7) + n8(-2 + n))(-3 + n) = 0 (80640 + -40320n + 57888n + -28944n2 + -40808n2 + 20404n3 + -60872n3 + 30436n4 + -28798n4 + 14399n5 + -7028n5 + 3514n6 + -952n6 + 476n7 + (-68n7 + 34n8) + n8(-2 + n))(-3 + n) = 0 (80640 + -40320n + 57888n + -28944n2 + -40808n2 + 20404n3 + -60872n3 + 30436n4 + -28798n4 + 14399n5 + -7028n5 + 3514n6 + -952n6 + 476n7 + -68n7 + 34n8 + (-2 * n8 + n * n8))(-3 + n) = 0 (80640 + -40320n + 57888n + -28944n2 + -40808n2 + 20404n3 + -60872n3 + 30436n4 + -28798n4 + 14399n5 + -7028n5 + 3514n6 + -952n6 + 476n7 + -68n7 + 34n8 + (-2n8 + n9))(-3 + n) = 0 Combine like terms: -40320n + 57888n = 17568n (80640 + 17568n + -28944n2 + -40808n2 + 20404n3 + -60872n3 + 30436n4 + -28798n4 + 14399n5 + -7028n5 + 3514n6 + -952n6 + 476n7 + -68n7 + 34n8 + -2n8 + n9)(-3 + n) = 0 Combine like terms: -28944n2 + -40808n2 = -69752n2 (80640 + 17568n + -69752n2 + 20404n3 + -60872n3 + 30436n4 + -28798n4 + 14399n5 + -7028n5 + 3514n6 + -952n6 + 476n7 + -68n7 + 34n8 + -2n8 + n9)(-3 + n) = 0 Combine like terms: 20404n3 + -60872n3 = -40468n3 (80640 + 17568n + -69752n2 + -40468n3 + 30436n4 + -28798n4 + 14399n5 + -7028n5 + 3514n6 + -952n6 + 476n7 + -68n7 + 34n8 + -2n8 + n9)(-3 + n) = 0 Combine like terms: 30436n4 + -28798n4 = 1638n4 (80640 + 17568n + -69752n2 + -40468n3 + 1638n4 + 14399n5 + -7028n5 + 3514n6 + -952n6 + 476n7 + -68n7 + 34n8 + -2n8 + n9)(-3 + n) = 0 Combine like terms: 14399n5 + -7028n5 = 7371n5 (80640 + 17568n + -69752n2 + -40468n3 + 1638n4 + 7371n5 + 3514n6 + -952n6 + 476n7 + -68n7 + 34n8 + -2n8 + n9)(-3 + n) = 0 Combine like terms: 3514n6 + -952n6 = 2562n6 (80640 + 17568n + -69752n2 + -40468n3 + 1638n4 + 7371n5 + 2562n6 + 476n7 + -68n7 + 34n8 + -2n8 + n9)(-3 + n) = 0 Combine like terms: 476n7 + -68n7 = 408n7 (80640 + 17568n + -69752n2 + -40468n3 + 1638n4 + 7371n5 + 2562n6 + 408n7 + 34n8 + -2n8 + n9)(-3 + n) = 0 Combine like terms: 34n8 + -2n8 = 32n8 (80640 + 17568n + -69752n2 + -40468n3 + 1638n4 + 7371n5 + 2562n6 + 408n7 + 32n8 + n9)(-3 + n) = 0 Multiply (80640 + 17568n + -69752n2 + -40468n3 + 1638n4 + 7371n5 + 2562n6 + 408n7 + 32n8 + n9) * (-3 + n) (80640(-3 + n) + 17568n * (-3 + n) + -69752n2 * (-3 + n) + -40468n3 * (-3 + n) + 1638n4 * (-3 + n) + 7371n5 * (-3 + n) + 2562n6 * (-3 + n) + 408n7 * (-3 + n) + 32n8 * (-3 + n) + n9(-3 + n)) = 0 ((-3 * 80640 + n * 80640) + 17568n * (-3 + n) + -69752n2 * (-3 + n) + -40468n3 * (-3 + n) + 1638n4 * (-3 + n) + 7371n5 * (-3 + n) + 2562n6 * (-3 + n) + 408n7 * (-3 + n) + 32n8 * (-3 + n) + n9(-3 + n)) = 0 ((-241920 + 80640n) + 17568n * (-3 + n) + -69752n2 * (-3 + n) + -40468n3 * (-3 + n) + 1638n4 * (-3 + n) + 7371n5 * (-3 + n) + 2562n6 * (-3 + n) + 408n7 * (-3 + n) + 32n8 * (-3 + n) + n9(-3 + n)) = 0 (-241920 + 80640n + (-3 * 17568n + n * 17568n) + -69752n2 * (-3 + n) + -40468n3 * (-3 + n) + 1638n4 * (-3 + n) + 7371n5 * (-3 + n) + 2562n6 * (-3 + n) + 408n7 * (-3 + n) + 32n8 * (-3 + n) + n9(-3 + n)) = 0 (-241920 + 80640n + (-52704n + 17568n2) + -69752n2 * (-3 + n) + -40468n3 * (-3 + n) + 1638n4 * (-3 + n) + 7371n5 * (-3 + n) + 2562n6 * (-3 + n) + 408n7 * (-3 + n) + 32n8 * (-3 + n) + n9(-3 + n)) = 0 (-241920 + 80640n + -52704n + 17568n2 + (-3 * -69752n2 + n * -69752n2) + -40468n3 * (-3 + n) + 1638n4 * (-3 + n) + 7371n5 * (-3 + n) + 2562n6 * (-3 + n) + 408n7 * (-3 + n) + 32n8 * (-3 + n) + n9(-3 + n)) = 0 (-241920 + 80640n + -52704n + 17568n2 + (209256n2 + -69752n3) + -40468n3 * (-3 + n) + 1638n4 * (-3 + n) + 7371n5 * (-3 + n) + 2562n6 * (-3 + n) + 408n7 * (-3 + n) + 32n8 * (-3 + n) + n9(-3 + n)) = 0 (-241920 + 80640n + -52704n + 17568n2 + 209256n2 + -69752n3 + (-3 * -40468n3 + n * -40468n3) + 1638n4 * (-3 + n) + 7371n5 * (-3 + n) + 2562n6 * (-3 + n) + 408n7 * (-3 + n) + 32n8 * (-3 + n) + n9(-3 + n)) = 0 (-241920 + 80640n + -52704n + 17568n2 + 209256n2 + -69752n3 + (121404n3 + -40468n4) + 1638n4 * (-3 + n) + 7371n5 * (-3 + n) + 2562n6 * (-3 + n) + 408n7 * (-3 + n) + 32n8 * (-3 + n) + n9(-3 + n)) = 0 (-241920 + 80640n + -52704n + 17568n2 + 209256n2 + -69752n3 + 121404n3 + -40468n4 + (-3 * 1638n4 + n * 1638n4) + 7371n5 * (-3 + n) + 2562n6 * (-3 + n) + 408n7 * (-3 + n) + 32n8 * (-3 + n) + n9(-3 + n)) = 0 (-241920 + 80640n + -52704n + 17568n2 + 209256n2 + -69752n3 + 121404n3 + -40468n4 + (-4914n4 + 1638n5) + 7371n5 * (-3 + n) + 2562n6 * (-3 + n) + 408n7 * (-3 + n) + 32n8 * (-3 + n) + n9(-3 + n)) = 0 (-241920 + 80640n + -52704n + 17568n2 + 209256n2 + -69752n3 + 121404n3 + -40468n4 + -4914n4 + 1638n5 + (-3 * 7371n5 + n * 7371n5) + 2562n6 * (-3 + n) + 408n7 * (-3 + n) + 32n8 * (-3 + n) + n9(-3 + n)) = 0 (-241920 + 80640n + -52704n + 17568n2 + 209256n2 + -69752n3 + 121404n3 + -40468n4 + -4914n4 + 1638n5 + (-22113n5 + 7371n6) + 2562n6 * (-3 + n) + 408n7 * (-3 + n) + 32n8 * (-3 + n) + n9(-3 + n)) = 0 (-241920 + 80640n + -52704n + 17568n2 + 209256n2 + -69752n3 + 121404n3 + -40468n4 + -4914n4 + 1638n5 + -22113n5 + 7371n6 + (-3 * 2562n6 + n * 2562n6) + 408n7 * (-3 + n) + 32n8 * (-3 + n) + n9(-3 + n)) = 0 (-241920 + 80640n + -52704n + 17568n2 + 209256n2 + -69752n3 + 121404n3 + -40468n4 + -4914n4 + 1638n5 + -22113n5 + 7371n6 + (-7686n6 + 2562n7) + 408n7 * (-3 + n) + 32n8 * (-3 + n) + n9(-3 + n)) = 0 (-241920 + 80640n + -52704n + 17568n2 + 209256n2 + -69752n3 + 121404n3 + -40468n4 + -4914n4 + 1638n5 + -22113n5 + 7371n6 + -7686n6 + 2562n7 + (-3 * 408n7 + n * 408n7) + 32n8 * (-3 + n) + n9(-3 + n)) = 0 (-241920 + 80640n + -52704n + 17568n2 + 209256n2 + -69752n3 + 121404n3 + -40468n4 + -4914n4 + 1638n5 + -22113n5 + 7371n6 + -7686n6 + 2562n7 + (-1224n7 + 408n8) + 32n8 * (-3 + n) + n9(-3 + n)) = 0 (-241920 + 80640n + -52704n + 17568n2 + 209256n2 + -69752n3 + 121404n3 + -40468n4 + -4914n4 + 1638n5 + -22113n5 + 7371n6 + -7686n6 + 2562n7 + -1224n7 + 408n8 + (-3 * 32n8 + n * 32n8) + n9(-3 + n)) = 0 (-241920 + 80640n + -52704n + 17568n2 + 209256n2 + -69752n3 + 121404n3 + -40468n4 + -4914n4 + 1638n5 + -22113n5 + 7371n6 + -7686n6 + 2562n7 + -1224n7 + 408n8 + (-96n8 + 32n9) + n9(-3 + n)) = 0 (-241920 + 80640n + -52704n + 17568n2 + 209256n2 + -69752n3 + 121404n3 + -40468n4 + -4914n4 + 1638n5 + -22113n5 + 7371n6 + -7686n6 + 2562n7 + -1224n7 + 408n8 + -96n8 + 32n9 + (-3 * n9 + n * n9)) = 0 (-241920 + 80640n + -52704n + 17568n2 + 209256n2 + -69752n3 + 121404n3 + -40468n4 + -4914n4 + 1638n5 + -22113n5 + 7371n6 + -7686n6 + 2562n7 + -1224n7 + 408n8 + -96n8 + 32n9 + (-3n9 + n10)) = 0 Combine like terms: 80640n + -52704n = 27936n (-241920 + 27936n + 17568n2 + 209256n2 + -69752n3 + 121404n3 + -40468n4 + -4914n4 + 1638n5 + -22113n5 + 7371n6 + -7686n6 + 2562n7 + -1224n7 + 408n8 + -96n8 + 32n9 + -3n9 + n10) = 0 Combine like terms: 17568n2 + 209256n2 = 226824n2 (-241920 + 27936n + 226824n2 + -69752n3 + 121404n3 + -40468n4 + -4914n4 + 1638n5 + -22113n5 + 7371n6 + -7686n6 + 2562n7 + -1224n7 + 408n8 + -96n8 + 32n9 + -3n9 + n10) = 0 Combine like terms: -69752n3 + 121404n3 = 51652n3 (-241920 + 27936n + 226824n2 + 51652n3 + -40468n4 + -4914n4 + 1638n5 + -22113n5 + 7371n6 + -7686n6 + 2562n7 + -1224n7 + 408n8 + -96n8 + 32n9 + -3n9 + n10) = 0 Combine like terms: -40468n4 + -4914n4 = -45382n4 (-241920 + 27936n + 226824n2 + 51652n3 + -45382n4 + 1638n5 + -22113n5 + 7371n6 + -7686n6 + 2562n7 + -1224n7 + 408n8 + -96n8 + 32n9 + -3n9 + n10) = 0 Combine like terms: 1638n5 + -22113n5 = -20475n5 (-241920 + 27936n + 226824n2 + 51652n3 + -45382n4 + -20475n5 + 7371n6 + -7686n6 + 2562n7 + -1224n7 + 408n8 + -96n8 + 32n9 + -3n9 + n10) = 0 Combine like terms: 7371n6 + -7686n6 = -315n6 (-241920 + 27936n + 226824n2 + 51652n3 + -45382n4 + -20475n5 + -315n6 + 2562n7 + -1224n7 + 408n8 + -96n8 + 32n9 + -3n9 + n10) = 0 Combine like terms: 2562n7 + -1224n7 = 1338n7 (-241920 + 27936n + 226824n2 + 51652n3 + -45382n4 + -20475n5 + -315n6 + 1338n7 + 408n8 + -96n8 + 32n9 + -3n9 + n10) = 0 Combine like terms: 408n8 + -96n8 = 312n8 (-241920 + 27936n + 226824n2 + 51652n3 + -45382n4 + -20475n5 + -315n6 + 1338n7 + 312n8 + 32n9 + -3n9 + n10) = 0 Combine like terms: 32n9 + -3n9 = 29n9 (-241920 + 27936n + 226824n2 + 51652n3 + -45382n4 + -20475n5 + -315n6 + 1338n7 + 312n8 + 29n9 + n10) = 0 Solving -241920 + 27936n + 226824n2 + 51652n3 + -45382n4 + -20475n5 + -315n6 + 1338n7 + 312n8 + 29n9 + n10 = 0 Solving for variable 'n'. The solution to this equation could not be determined.
| 8A+3(2A)=120 | | 6x+2(x+2)=46 | | 3i(4+2i)= | | 2x^2+3x^3-5=0 | | 1/9x-(2x+7)=0 | | (9+n)(8+n)(7+n)(6+n)(5+n)(4+n)(3+n)(2+n)(n-1)(n-2)=0 | | 17-x=1/3*3 | | 2x^2+-1= | | 17-x=1/3*17+6 | | y=3mx-8b | | 7x+4=58 | | 4ln(5x+5)=2 | | 8+3lnx=5 | | 2x+36x=90 | | (x+12)(y+12)=169 | | 3x+(-5)=55 | | y^2+5y-26=0 | | 1/2(x-7)=5 | | 10x^2+20x-18=0 | | 3x-2(x+y)= | | (2a-3b-4c)(2a-3b)=0 | | -5x^2+-8x^2=121 | | 40x+40y= | | 72-x=36 | | 5(x-y)=65 | | 12x^3+4x-3=0 | | 9x^2+12=3x^2-24 | | 3x-9=6+4x | | ydx-(x+y^2)dy=0 | | 3x-9=6+4 | | g(x)=0(0)(0)-5 | | g(x)=4(4)(4)-5 |