(8+n)(7+n)(6+n)(5+n)(4+n)(3+n)(2+n)(n-1)=0

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Solution for (8+n)(7+n)(6+n)(5+n)(4+n)(3+n)(2+n)(n-1)=0 equation:


Simplifying
(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(n + -1) = 0

Reorder the terms:
(8 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + 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) = 0
((7 * 8 + n * 8) + n(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0
((56 + 8n) + n(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0
(56 + 8n + (7 * n + n * n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0
(56 + 8n + (7n + n2))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0

Combine like terms: 8n + 7n = 15n
(56 + 15n + n2)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + 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) = 0
((6 * 56 + n * 56) + 15n * (6 + n) + n2(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0
((336 + 56n) + 15n * (6 + n) + n2(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0
(336 + 56n + (6 * 15n + n * 15n) + n2(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0
(336 + 56n + (90n + 15n2) + n2(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0
(336 + 56n + 90n + 15n2 + (6 * n2 + n * n2))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0
(336 + 56n + 90n + 15n2 + (6n2 + n3))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0

Combine like terms: 56n + 90n = 146n
(336 + 146n + 15n2 + 6n2 + n3)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n) = 0

Combine like terms: 15n2 + 6n2 = 21n2
(336 + 146n + 21n2 + n3)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + 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) = 0
((5 * 336 + n * 336) + 146n * (5 + n) + 21n2 * (5 + n) + n3(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n) = 0
((1680 + 336n) + 146n * (5 + n) + 21n2 * (5 + n) + n3(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n) = 0
(1680 + 336n + (5 * 146n + n * 146n) + 21n2 * (5 + n) + n3(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n) = 0
(1680 + 336n + (730n + 146n2) + 21n2 * (5 + n) + n3(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n) = 0
(1680 + 336n + 730n + 146n2 + (5 * 21n2 + n * 21n2) + n3(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n) = 0
(1680 + 336n + 730n + 146n2 + (105n2 + 21n3) + n3(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n) = 0
(1680 + 336n + 730n + 146n2 + 105n2 + 21n3 + (5 * n3 + n * n3))(4 + n)(3 + n)(2 + n)(-1 + n) = 0
(1680 + 336n + 730n + 146n2 + 105n2 + 21n3 + (5n3 + n4))(4 + n)(3 + n)(2 + n)(-1 + n) = 0

Combine like terms: 336n + 730n = 1066n
(1680 + 1066n + 146n2 + 105n2 + 21n3 + 5n3 + n4)(4 + n)(3 + n)(2 + n)(-1 + n) = 0

Combine like terms: 146n2 + 105n2 = 251n2
(1680 + 1066n + 251n2 + 21n3 + 5n3 + n4)(4 + n)(3 + n)(2 + n)(-1 + n) = 0

Combine like terms: 21n3 + 5n3 = 26n3
(1680 + 1066n + 251n2 + 26n3 + n4)(4 + n)(3 + n)(2 + n)(-1 + 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) = 0
((4 * 1680 + n * 1680) + 1066n * (4 + n) + 251n2 * (4 + n) + 26n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n) = 0
((6720 + 1680n) + 1066n * (4 + n) + 251n2 * (4 + n) + 26n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n) = 0
(6720 + 1680n + (4 * 1066n + n * 1066n) + 251n2 * (4 + n) + 26n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n) = 0
(6720 + 1680n + (4264n + 1066n2) + 251n2 * (4 + n) + 26n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n) = 0
(6720 + 1680n + 4264n + 1066n2 + (4 * 251n2 + n * 251n2) + 26n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n) = 0
(6720 + 1680n + 4264n + 1066n2 + (1004n2 + 251n3) + 26n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n) = 0
(6720 + 1680n + 4264n + 1066n2 + 1004n2 + 251n3 + (4 * 26n3 + n * 26n3) + n4(4 + n))(3 + n)(2 + n)(-1 + n) = 0
(6720 + 1680n + 4264n + 1066n2 + 1004n2 + 251n3 + (104n3 + 26n4) + n4(4 + n))(3 + n)(2 + n)(-1 + n) = 0
(6720 + 1680n + 4264n + 1066n2 + 1004n2 + 251n3 + 104n3 + 26n4 + (4 * n4 + n * n4))(3 + n)(2 + n)(-1 + n) = 0
(6720 + 1680n + 4264n + 1066n2 + 1004n2 + 251n3 + 104n3 + 26n4 + (4n4 + n5))(3 + n)(2 + n)(-1 + n) = 0

Combine like terms: 1680n + 4264n = 5944n
(6720 + 5944n + 1066n2 + 1004n2 + 251n3 + 104n3 + 26n4 + 4n4 + n5)(3 + n)(2 + n)(-1 + n) = 0

Combine like terms: 1066n2 + 1004n2 = 2070n2
(6720 + 5944n + 2070n2 + 251n3 + 104n3 + 26n4 + 4n4 + n5)(3 + n)(2 + n)(-1 + n) = 0

Combine like terms: 251n3 + 104n3 = 355n3
(6720 + 5944n + 2070n2 + 355n3 + 26n4 + 4n4 + n5)(3 + n)(2 + n)(-1 + n) = 0

Combine like terms: 26n4 + 4n4 = 30n4
(6720 + 5944n + 2070n2 + 355n3 + 30n4 + n5)(3 + n)(2 + n)(-1 + 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) = 0
((3 * 6720 + n * 6720) + 5944n * (3 + n) + 2070n2 * (3 + n) + 355n3 * (3 + n) + 30n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n) = 0
((20160 + 6720n) + 5944n * (3 + n) + 2070n2 * (3 + n) + 355n3 * (3 + n) + 30n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n) = 0
(20160 + 6720n + (3 * 5944n + n * 5944n) + 2070n2 * (3 + n) + 355n3 * (3 + n) + 30n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n) = 0
(20160 + 6720n + (17832n + 5944n2) + 2070n2 * (3 + n) + 355n3 * (3 + n) + 30n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n) = 0
(20160 + 6720n + 17832n + 5944n2 + (3 * 2070n2 + n * 2070n2) + 355n3 * (3 + n) + 30n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n) = 0
(20160 + 6720n + 17832n + 5944n2 + (6210n2 + 2070n3) + 355n3 * (3 + n) + 30n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n) = 0
(20160 + 6720n + 17832n + 5944n2 + 6210n2 + 2070n3 + (3 * 355n3 + n * 355n3) + 30n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n) = 0
(20160 + 6720n + 17832n + 5944n2 + 6210n2 + 2070n3 + (1065n3 + 355n4) + 30n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n) = 0
(20160 + 6720n + 17832n + 5944n2 + 6210n2 + 2070n3 + 1065n3 + 355n4 + (3 * 30n4 + n * 30n4) + n5(3 + n))(2 + n)(-1 + n) = 0
(20160 + 6720n + 17832n + 5944n2 + 6210n2 + 2070n3 + 1065n3 + 355n4 + (90n4 + 30n5) + n5(3 + n))(2 + n)(-1 + n) = 0
(20160 + 6720n + 17832n + 5944n2 + 6210n2 + 2070n3 + 1065n3 + 355n4 + 90n4 + 30n5 + (3 * n5 + n * n5))(2 + n)(-1 + n) = 0
(20160 + 6720n + 17832n + 5944n2 + 6210n2 + 2070n3 + 1065n3 + 355n4 + 90n4 + 30n5 + (3n5 + n6))(2 + n)(-1 + n) = 0

Combine like terms: 6720n + 17832n = 24552n
(20160 + 24552n + 5944n2 + 6210n2 + 2070n3 + 1065n3 + 355n4 + 90n4 + 30n5 + 3n5 + n6)(2 + n)(-1 + n) = 0

Combine like terms: 5944n2 + 6210n2 = 12154n2
(20160 + 24552n + 12154n2 + 2070n3 + 1065n3 + 355n4 + 90n4 + 30n5 + 3n5 + n6)(2 + n)(-1 + n) = 0

Combine like terms: 2070n3 + 1065n3 = 3135n3
(20160 + 24552n + 12154n2 + 3135n3 + 355n4 + 90n4 + 30n5 + 3n5 + n6)(2 + n)(-1 + n) = 0

Combine like terms: 355n4 + 90n4 = 445n4
(20160 + 24552n + 12154n2 + 3135n3 + 445n4 + 30n5 + 3n5 + n6)(2 + n)(-1 + n) = 0

Combine like terms: 30n5 + 3n5 = 33n5
(20160 + 24552n + 12154n2 + 3135n3 + 445n4 + 33n5 + n6)(2 + n)(-1 + 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) = 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) = 0
((40320 + 20160n) + 24552n * (2 + n) + 12154n2 * (2 + n) + 3135n3 * (2 + n) + 445n4 * (2 + n) + 33n5 * (2 + n) + n6(2 + n))(-1 + 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) = 0
(40320 + 20160n + (49104n + 24552n2) + 12154n2 * (2 + n) + 3135n3 * (2 + n) + 445n4 * (2 + n) + 33n5 * (2 + n) + n6(2 + n))(-1 + n) = 0
(40320 + 20160n + 49104n + 24552n2 + (2 * 12154n2 + n * 12154n2) + 3135n3 * (2 + n) + 445n4 * (2 + n) + 33n5 * (2 + n) + n6(2 + n))(-1 + n) = 0
(40320 + 20160n + 49104n + 24552n2 + (24308n2 + 12154n3) + 3135n3 * (2 + n) + 445n4 * (2 + n) + 33n5 * (2 + n) + n6(2 + n))(-1 + n) = 0
(40320 + 20160n + 49104n + 24552n2 + 24308n2 + 12154n3 + (2 * 3135n3 + n * 3135n3) + 445n4 * (2 + n) + 33n5 * (2 + n) + n6(2 + n))(-1 + n) = 0
(40320 + 20160n + 49104n + 24552n2 + 24308n2 + 12154n3 + (6270n3 + 3135n4) + 445n4 * (2 + n) + 33n5 * (2 + n) + n6(2 + n))(-1 + n) = 0
(40320 + 20160n + 49104n + 24552n2 + 24308n2 + 12154n3 + 6270n3 + 3135n4 + (2 * 445n4 + n * 445n4) + 33n5 * (2 + n) + n6(2 + n))(-1 + n) = 0
(40320 + 20160n + 49104n + 24552n2 + 24308n2 + 12154n3 + 6270n3 + 3135n4 + (890n4 + 445n5) + 33n5 * (2 + n) + n6(2 + n))(-1 + n) = 0
(40320 + 20160n + 49104n + 24552n2 + 24308n2 + 12154n3 + 6270n3 + 3135n4 + 890n4 + 445n5 + (2 * 33n5 + n * 33n5) + n6(2 + n))(-1 + n) = 0
(40320 + 20160n + 49104n + 24552n2 + 24308n2 + 12154n3 + 6270n3 + 3135n4 + 890n4 + 445n5 + (66n5 + 33n6) + n6(2 + n))(-1 + n) = 0
(40320 + 20160n + 49104n + 24552n2 + 24308n2 + 12154n3 + 6270n3 + 3135n4 + 890n4 + 445n5 + 66n5 + 33n6 + (2 * n6 + n * n6))(-1 + n) = 0
(40320 + 20160n + 49104n + 24552n2 + 24308n2 + 12154n3 + 6270n3 + 3135n4 + 890n4 + 445n5 + 66n5 + 33n6 + (2n6 + n7))(-1 + n) = 0

Combine like terms: 20160n + 49104n = 69264n
(40320 + 69264n + 24552n2 + 24308n2 + 12154n3 + 6270n3 + 3135n4 + 890n4 + 445n5 + 66n5 + 33n6 + 2n6 + n7)(-1 + n) = 0

Combine like terms: 24552n2 + 24308n2 = 48860n2
(40320 + 69264n + 48860n2 + 12154n3 + 6270n3 + 3135n4 + 890n4 + 445n5 + 66n5 + 33n6 + 2n6 + n7)(-1 + n) = 0

Combine like terms: 12154n3 + 6270n3 = 18424n3
(40320 + 69264n + 48860n2 + 18424n3 + 3135n4 + 890n4 + 445n5 + 66n5 + 33n6 + 2n6 + n7)(-1 + n) = 0

Combine like terms: 3135n4 + 890n4 = 4025n4
(40320 + 69264n + 48860n2 + 18424n3 + 4025n4 + 445n5 + 66n5 + 33n6 + 2n6 + n7)(-1 + n) = 0

Combine like terms: 445n5 + 66n5 = 511n5
(40320 + 69264n + 48860n2 + 18424n3 + 4025n4 + 511n5 + 33n6 + 2n6 + n7)(-1 + n) = 0

Combine like terms: 33n6 + 2n6 = 35n6
(40320 + 69264n + 48860n2 + 18424n3 + 4025n4 + 511n5 + 35n6 + n7)(-1 + 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)) = 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)) = 0
((-40320 + 40320n) + 69264n * (-1 + n) + 48860n2 * (-1 + n) + 18424n3 * (-1 + n) + 4025n4 * (-1 + n) + 511n5 * (-1 + n) + 35n6 * (-1 + n) + n7(-1 + 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)) = 0
(-40320 + 40320n + (-69264n + 69264n2) + 48860n2 * (-1 + n) + 18424n3 * (-1 + n) + 4025n4 * (-1 + n) + 511n5 * (-1 + n) + 35n6 * (-1 + n) + n7(-1 + 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)) = 0
(-40320 + 40320n + -69264n + 69264n2 + (-48860n2 + 48860n3) + 18424n3 * (-1 + n) + 4025n4 * (-1 + n) + 511n5 * (-1 + n) + 35n6 * (-1 + n) + n7(-1 + n)) = 0
(-40320 + 40320n + -69264n + 69264n2 + -48860n2 + 48860n3 + (-1 * 18424n3 + n * 18424n3) + 4025n4 * (-1 + n) + 511n5 * (-1 + n) + 35n6 * (-1 + n) + n7(-1 + n)) = 0
(-40320 + 40320n + -69264n + 69264n2 + -48860n2 + 48860n3 + (-18424n3 + 18424n4) + 4025n4 * (-1 + n) + 511n5 * (-1 + n) + 35n6 * (-1 + n) + n7(-1 + n)) = 0
(-40320 + 40320n + -69264n + 69264n2 + -48860n2 + 48860n3 + -18424n3 + 18424n4 + (-1 * 4025n4 + n * 4025n4) + 511n5 * (-1 + n) + 35n6 * (-1 + n) + n7(-1 + n)) = 0
(-40320 + 40320n + -69264n + 69264n2 + -48860n2 + 48860n3 + -18424n3 + 18424n4 + (-4025n4 + 4025n5) + 511n5 * (-1 + n) + 35n6 * (-1 + n) + n7(-1 + n)) = 0
(-40320 + 40320n + -69264n + 69264n2 + -48860n2 + 48860n3 + -18424n3 + 18424n4 + -4025n4 + 4025n5 + (-1 * 511n5 + n * 511n5) + 35n6 * (-1 + n) + n7(-1 + n)) = 0
(-40320 + 40320n + -69264n + 69264n2 + -48860n2 + 48860n3 + -18424n3 + 18424n4 + -4025n4 + 4025n5 + (-511n5 + 511n6) + 35n6 * (-1 + n) + n7(-1 + n)) = 0
(-40320 + 40320n + -69264n + 69264n2 + -48860n2 + 48860n3 + -18424n3 + 18424n4 + -4025n4 + 4025n5 + -511n5 + 511n6 + (-1 * 35n6 + n * 35n6) + n7(-1 + n)) = 0
(-40320 + 40320n + -69264n + 69264n2 + -48860n2 + 48860n3 + -18424n3 + 18424n4 + -4025n4 + 4025n5 + -511n5 + 511n6 + (-35n6 + 35n7) + n7(-1 + n)) = 0
(-40320 + 40320n + -69264n + 69264n2 + -48860n2 + 48860n3 + -18424n3 + 18424n4 + -4025n4 + 4025n5 + -511n5 + 511n6 + -35n6 + 35n7 + (-1 * n7 + n * n7)) = 0
(-40320 + 40320n + -69264n + 69264n2 + -48860n2 + 48860n3 + -18424n3 + 18424n4 + -4025n4 + 4025n5 + -511n5 + 511n6 + -35n6 + 35n7 + (-1n7 + n8)) = 0

Combine like terms: 40320n + -69264n = -28944n
(-40320 + -28944n + 69264n2 + -48860n2 + 48860n3 + -18424n3 + 18424n4 + -4025n4 + 4025n5 + -511n5 + 511n6 + -35n6 + 35n7 + -1n7 + n8) = 0

Combine like terms: 69264n2 + -48860n2 = 20404n2
(-40320 + -28944n + 20404n2 + 48860n3 + -18424n3 + 18424n4 + -4025n4 + 4025n5 + -511n5 + 511n6 + -35n6 + 35n7 + -1n7 + n8) = 0

Combine like terms: 48860n3 + -18424n3 = 30436n3
(-40320 + -28944n + 20404n2 + 30436n3 + 18424n4 + -4025n4 + 4025n5 + -511n5 + 511n6 + -35n6 + 35n7 + -1n7 + n8) = 0

Combine like terms: 18424n4 + -4025n4 = 14399n4
(-40320 + -28944n + 20404n2 + 30436n3 + 14399n4 + 4025n5 + -511n5 + 511n6 + -35n6 + 35n7 + -1n7 + n8) = 0

Combine like terms: 4025n5 + -511n5 = 3514n5
(-40320 + -28944n + 20404n2 + 30436n3 + 14399n4 + 3514n5 + 511n6 + -35n6 + 35n7 + -1n7 + n8) = 0

Combine like terms: 511n6 + -35n6 = 476n6
(-40320 + -28944n + 20404n2 + 30436n3 + 14399n4 + 3514n5 + 476n6 + 35n7 + -1n7 + n8) = 0

Combine like terms: 35n7 + -1n7 = 34n7
(-40320 + -28944n + 20404n2 + 30436n3 + 14399n4 + 3514n5 + 476n6 + 34n7 + n8) = 0

Solving
-40320 + -28944n + 20404n2 + 30436n3 + 14399n4 + 3514n5 + 476n6 + 34n7 + n8 = 0

Solving for variable 'n'.

The solution to this equation could not be determined.

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