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

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


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

Reorder the terms:
(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(n + -2)(n + -3)(n + -4) = 0

Reorder the terms:
(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(n + -3)(n + -4) = 0

Reorder the terms:
(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n)(n + -4) = 0

Reorder the terms:
(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0

Multiply (5 + n) * (4 + n)
(5(4 + n) + n(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0
((4 * 5 + n * 5) + n(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0
((20 + 5n) + n(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0
(20 + 5n + (4 * n + n * n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0
(20 + 5n + (4n + n2))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0

Combine like terms: 5n + 4n = 9n
(20 + 9n + n2)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0

Multiply (20 + 9n + n2) * (3 + n)
(20(3 + n) + 9n * (3 + n) + n2(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0
((3 * 20 + n * 20) + 9n * (3 + n) + n2(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0
((60 + 20n) + 9n * (3 + n) + n2(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0
(60 + 20n + (3 * 9n + n * 9n) + n2(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0
(60 + 20n + (27n + 9n2) + n2(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0
(60 + 20n + 27n + 9n2 + (3 * n2 + n * n2))(2 + n)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0
(60 + 20n + 27n + 9n2 + (3n2 + n3))(2 + n)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0

Combine like terms: 20n + 27n = 47n
(60 + 47n + 9n2 + 3n2 + n3)(2 + n)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0

Combine like terms: 9n2 + 3n2 = 12n2
(60 + 47n + 12n2 + n3)(2 + n)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0

Multiply (60 + 47n + 12n2 + n3) * (2 + n)
(60(2 + n) + 47n * (2 + n) + 12n2 * (2 + n) + n3(2 + n))(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0
((2 * 60 + n * 60) + 47n * (2 + n) + 12n2 * (2 + n) + n3(2 + n))(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0
((120 + 60n) + 47n * (2 + n) + 12n2 * (2 + n) + n3(2 + n))(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0
(120 + 60n + (2 * 47n + n * 47n) + 12n2 * (2 + n) + n3(2 + n))(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0
(120 + 60n + (94n + 47n2) + 12n2 * (2 + n) + n3(2 + n))(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0
(120 + 60n + 94n + 47n2 + (2 * 12n2 + n * 12n2) + n3(2 + n))(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0
(120 + 60n + 94n + 47n2 + (24n2 + 12n3) + n3(2 + n))(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0
(120 + 60n + 94n + 47n2 + 24n2 + 12n3 + (2 * n3 + n * n3))(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0
(120 + 60n + 94n + 47n2 + 24n2 + 12n3 + (2n3 + n4))(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0

Combine like terms: 60n + 94n = 154n
(120 + 154n + 47n2 + 24n2 + 12n3 + 2n3 + n4)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0

Combine like terms: 47n2 + 24n2 = 71n2
(120 + 154n + 71n2 + 12n3 + 2n3 + n4)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0

Combine like terms: 12n3 + 2n3 = 14n3
(120 + 154n + 71n2 + 14n3 + n4)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0

Multiply (120 + 154n + 71n2 + 14n3 + n4) * (-1 + n)
(120(-1 + n) + 154n * (-1 + n) + 71n2 * (-1 + n) + 14n3 * (-1 + n) + n4(-1 + n))(-2 + n)(-3 + n)(-4 + n) = 0
((-1 * 120 + n * 120) + 154n * (-1 + n) + 71n2 * (-1 + n) + 14n3 * (-1 + n) + n4(-1 + n))(-2 + n)(-3 + n)(-4 + n) = 0
((-120 + 120n) + 154n * (-1 + n) + 71n2 * (-1 + n) + 14n3 * (-1 + n) + n4(-1 + n))(-2 + n)(-3 + n)(-4 + n) = 0
(-120 + 120n + (-1 * 154n + n * 154n) + 71n2 * (-1 + n) + 14n3 * (-1 + n) + n4(-1 + n))(-2 + n)(-3 + n)(-4 + n) = 0
(-120 + 120n + (-154n + 154n2) + 71n2 * (-1 + n) + 14n3 * (-1 + n) + n4(-1 + n))(-2 + n)(-3 + n)(-4 + n) = 0
(-120 + 120n + -154n + 154n2 + (-1 * 71n2 + n * 71n2) + 14n3 * (-1 + n) + n4(-1 + n))(-2 + n)(-3 + n)(-4 + n) = 0
(-120 + 120n + -154n + 154n2 + (-71n2 + 71n3) + 14n3 * (-1 + n) + n4(-1 + n))(-2 + n)(-3 + n)(-4 + n) = 0
(-120 + 120n + -154n + 154n2 + -71n2 + 71n3 + (-1 * 14n3 + n * 14n3) + n4(-1 + n))(-2 + n)(-3 + n)(-4 + n) = 0
(-120 + 120n + -154n + 154n2 + -71n2 + 71n3 + (-14n3 + 14n4) + n4(-1 + n))(-2 + n)(-3 + n)(-4 + n) = 0
(-120 + 120n + -154n + 154n2 + -71n2 + 71n3 + -14n3 + 14n4 + (-1 * n4 + n * n4))(-2 + n)(-3 + n)(-4 + n) = 0
(-120 + 120n + -154n + 154n2 + -71n2 + 71n3 + -14n3 + 14n4 + (-1n4 + n5))(-2 + n)(-3 + n)(-4 + n) = 0

Combine like terms: 120n + -154n = -34n
(-120 + -34n + 154n2 + -71n2 + 71n3 + -14n3 + 14n4 + -1n4 + n5)(-2 + n)(-3 + n)(-4 + n) = 0

Combine like terms: 154n2 + -71n2 = 83n2
(-120 + -34n + 83n2 + 71n3 + -14n3 + 14n4 + -1n4 + n5)(-2 + n)(-3 + n)(-4 + n) = 0

Combine like terms: 71n3 + -14n3 = 57n3
(-120 + -34n + 83n2 + 57n3 + 14n4 + -1n4 + n5)(-2 + n)(-3 + n)(-4 + n) = 0

Combine like terms: 14n4 + -1n4 = 13n4
(-120 + -34n + 83n2 + 57n3 + 13n4 + n5)(-2 + n)(-3 + n)(-4 + n) = 0

Multiply (-120 + -34n + 83n2 + 57n3 + 13n4 + n5) * (-2 + n)
(-120(-2 + n) + -34n * (-2 + n) + 83n2 * (-2 + n) + 57n3 * (-2 + n) + 13n4 * (-2 + n) + n5(-2 + n))(-3 + n)(-4 + n) = 0
((-2 * -120 + n * -120) + -34n * (-2 + n) + 83n2 * (-2 + n) + 57n3 * (-2 + n) + 13n4 * (-2 + n) + n5(-2 + n))(-3 + n)(-4 + n) = 0
((240 + -120n) + -34n * (-2 + n) + 83n2 * (-2 + n) + 57n3 * (-2 + n) + 13n4 * (-2 + n) + n5(-2 + n))(-3 + n)(-4 + n) = 0
(240 + -120n + (-2 * -34n + n * -34n) + 83n2 * (-2 + n) + 57n3 * (-2 + n) + 13n4 * (-2 + n) + n5(-2 + n))(-3 + n)(-4 + n) = 0
(240 + -120n + (68n + -34n2) + 83n2 * (-2 + n) + 57n3 * (-2 + n) + 13n4 * (-2 + n) + n5(-2 + n))(-3 + n)(-4 + n) = 0
(240 + -120n + 68n + -34n2 + (-2 * 83n2 + n * 83n2) + 57n3 * (-2 + n) + 13n4 * (-2 + n) + n5(-2 + n))(-3 + n)(-4 + n) = 0
(240 + -120n + 68n + -34n2 + (-166n2 + 83n3) + 57n3 * (-2 + n) + 13n4 * (-2 + n) + n5(-2 + n))(-3 + n)(-4 + n) = 0
(240 + -120n + 68n + -34n2 + -166n2 + 83n3 + (-2 * 57n3 + n * 57n3) + 13n4 * (-2 + n) + n5(-2 + n))(-3 + n)(-4 + n) = 0
(240 + -120n + 68n + -34n2 + -166n2 + 83n3 + (-114n3 + 57n4) + 13n4 * (-2 + n) + n5(-2 + n))(-3 + n)(-4 + n) = 0
(240 + -120n + 68n + -34n2 + -166n2 + 83n3 + -114n3 + 57n4 + (-2 * 13n4 + n * 13n4) + n5(-2 + n))(-3 + n)(-4 + n) = 0
(240 + -120n + 68n + -34n2 + -166n2 + 83n3 + -114n3 + 57n4 + (-26n4 + 13n5) + n5(-2 + n))(-3 + n)(-4 + n) = 0
(240 + -120n + 68n + -34n2 + -166n2 + 83n3 + -114n3 + 57n4 + -26n4 + 13n5 + (-2 * n5 + n * n5))(-3 + n)(-4 + n) = 0
(240 + -120n + 68n + -34n2 + -166n2 + 83n3 + -114n3 + 57n4 + -26n4 + 13n5 + (-2n5 + n6))(-3 + n)(-4 + n) = 0

Combine like terms: -120n + 68n = -52n
(240 + -52n + -34n2 + -166n2 + 83n3 + -114n3 + 57n4 + -26n4 + 13n5 + -2n5 + n6)(-3 + n)(-4 + n) = 0

Combine like terms: -34n2 + -166n2 = -200n2
(240 + -52n + -200n2 + 83n3 + -114n3 + 57n4 + -26n4 + 13n5 + -2n5 + n6)(-3 + n)(-4 + n) = 0

Combine like terms: 83n3 + -114n3 = -31n3
(240 + -52n + -200n2 + -31n3 + 57n4 + -26n4 + 13n5 + -2n5 + n6)(-3 + n)(-4 + n) = 0

Combine like terms: 57n4 + -26n4 = 31n4
(240 + -52n + -200n2 + -31n3 + 31n4 + 13n5 + -2n5 + n6)(-3 + n)(-4 + n) = 0

Combine like terms: 13n5 + -2n5 = 11n5
(240 + -52n + -200n2 + -31n3 + 31n4 + 11n5 + n6)(-3 + n)(-4 + n) = 0

Multiply (240 + -52n + -200n2 + -31n3 + 31n4 + 11n5 + n6) * (-3 + n)
(240(-3 + n) + -52n * (-3 + n) + -200n2 * (-3 + n) + -31n3 * (-3 + n) + 31n4 * (-3 + n) + 11n5 * (-3 + n) + n6(-3 + n))(-4 + n) = 0
((-3 * 240 + n * 240) + -52n * (-3 + n) + -200n2 * (-3 + n) + -31n3 * (-3 + n) + 31n4 * (-3 + n) + 11n5 * (-3 + n) + n6(-3 + n))(-4 + n) = 0
((-720 + 240n) + -52n * (-3 + n) + -200n2 * (-3 + n) + -31n3 * (-3 + n) + 31n4 * (-3 + n) + 11n5 * (-3 + n) + n6(-3 + n))(-4 + n) = 0
(-720 + 240n + (-3 * -52n + n * -52n) + -200n2 * (-3 + n) + -31n3 * (-3 + n) + 31n4 * (-3 + n) + 11n5 * (-3 + n) + n6(-3 + n))(-4 + n) = 0
(-720 + 240n + (156n + -52n2) + -200n2 * (-3 + n) + -31n3 * (-3 + n) + 31n4 * (-3 + n) + 11n5 * (-3 + n) + n6(-3 + n))(-4 + n) = 0
(-720 + 240n + 156n + -52n2 + (-3 * -200n2 + n * -200n2) + -31n3 * (-3 + n) + 31n4 * (-3 + n) + 11n5 * (-3 + n) + n6(-3 + n))(-4 + n) = 0
(-720 + 240n + 156n + -52n2 + (600n2 + -200n3) + -31n3 * (-3 + n) + 31n4 * (-3 + n) + 11n5 * (-3 + n) + n6(-3 + n))(-4 + n) = 0
(-720 + 240n + 156n + -52n2 + 600n2 + -200n3 + (-3 * -31n3 + n * -31n3) + 31n4 * (-3 + n) + 11n5 * (-3 + n) + n6(-3 + n))(-4 + n) = 0
(-720 + 240n + 156n + -52n2 + 600n2 + -200n3 + (93n3 + -31n4) + 31n4 * (-3 + n) + 11n5 * (-3 + n) + n6(-3 + n))(-4 + n) = 0
(-720 + 240n + 156n + -52n2 + 600n2 + -200n3 + 93n3 + -31n4 + (-3 * 31n4 + n * 31n4) + 11n5 * (-3 + n) + n6(-3 + n))(-4 + n) = 0
(-720 + 240n + 156n + -52n2 + 600n2 + -200n3 + 93n3 + -31n4 + (-93n4 + 31n5) + 11n5 * (-3 + n) + n6(-3 + n))(-4 + n) = 0
(-720 + 240n + 156n + -52n2 + 600n2 + -200n3 + 93n3 + -31n4 + -93n4 + 31n5 + (-3 * 11n5 + n * 11n5) + n6(-3 + n))(-4 + n) = 0
(-720 + 240n + 156n + -52n2 + 600n2 + -200n3 + 93n3 + -31n4 + -93n4 + 31n5 + (-33n5 + 11n6) + n6(-3 + n))(-4 + n) = 0
(-720 + 240n + 156n + -52n2 + 600n2 + -200n3 + 93n3 + -31n4 + -93n4 + 31n5 + -33n5 + 11n6 + (-3 * n6 + n * n6))(-4 + n) = 0
(-720 + 240n + 156n + -52n2 + 600n2 + -200n3 + 93n3 + -31n4 + -93n4 + 31n5 + -33n5 + 11n6 + (-3n6 + n7))(-4 + n) = 0

Combine like terms: 240n + 156n = 396n
(-720 + 396n + -52n2 + 600n2 + -200n3 + 93n3 + -31n4 + -93n4 + 31n5 + -33n5 + 11n6 + -3n6 + n7)(-4 + n) = 0

Combine like terms: -52n2 + 600n2 = 548n2
(-720 + 396n + 548n2 + -200n3 + 93n3 + -31n4 + -93n4 + 31n5 + -33n5 + 11n6 + -3n6 + n7)(-4 + n) = 0

Combine like terms: -200n3 + 93n3 = -107n3
(-720 + 396n + 548n2 + -107n3 + -31n4 + -93n4 + 31n5 + -33n5 + 11n6 + -3n6 + n7)(-4 + n) = 0

Combine like terms: -31n4 + -93n4 = -124n4
(-720 + 396n + 548n2 + -107n3 + -124n4 + 31n5 + -33n5 + 11n6 + -3n6 + n7)(-4 + n) = 0

Combine like terms: 31n5 + -33n5 = -2n5
(-720 + 396n + 548n2 + -107n3 + -124n4 + -2n5 + 11n6 + -3n6 + n7)(-4 + n) = 0

Combine like terms: 11n6 + -3n6 = 8n6
(-720 + 396n + 548n2 + -107n3 + -124n4 + -2n5 + 8n6 + n7)(-4 + n) = 0

Multiply (-720 + 396n + 548n2 + -107n3 + -124n4 + -2n5 + 8n6 + n7) * (-4 + n)
(-720(-4 + n) + 396n * (-4 + n) + 548n2 * (-4 + n) + -107n3 * (-4 + n) + -124n4 * (-4 + n) + -2n5 * (-4 + n) + 8n6 * (-4 + n) + n7(-4 + n)) = 0
((-4 * -720 + n * -720) + 396n * (-4 + n) + 548n2 * (-4 + n) + -107n3 * (-4 + n) + -124n4 * (-4 + n) + -2n5 * (-4 + n) + 8n6 * (-4 + n) + n7(-4 + n)) = 0
((2880 + -720n) + 396n * (-4 + n) + 548n2 * (-4 + n) + -107n3 * (-4 + n) + -124n4 * (-4 + n) + -2n5 * (-4 + n) + 8n6 * (-4 + n) + n7(-4 + n)) = 0
(2880 + -720n + (-4 * 396n + n * 396n) + 548n2 * (-4 + n) + -107n3 * (-4 + n) + -124n4 * (-4 + n) + -2n5 * (-4 + n) + 8n6 * (-4 + n) + n7(-4 + n)) = 0
(2880 + -720n + (-1584n + 396n2) + 548n2 * (-4 + n) + -107n3 * (-4 + n) + -124n4 * (-4 + n) + -2n5 * (-4 + n) + 8n6 * (-4 + n) + n7(-4 + n)) = 0
(2880 + -720n + -1584n + 396n2 + (-4 * 548n2 + n * 548n2) + -107n3 * (-4 + n) + -124n4 * (-4 + n) + -2n5 * (-4 + n) + 8n6 * (-4 + n) + n7(-4 + n)) = 0
(2880 + -720n + -1584n + 396n2 + (-2192n2 + 548n3) + -107n3 * (-4 + n) + -124n4 * (-4 + n) + -2n5 * (-4 + n) + 8n6 * (-4 + n) + n7(-4 + n)) = 0
(2880 + -720n + -1584n + 396n2 + -2192n2 + 548n3 + (-4 * -107n3 + n * -107n3) + -124n4 * (-4 + n) + -2n5 * (-4 + n) + 8n6 * (-4 + n) + n7(-4 + n)) = 0
(2880 + -720n + -1584n + 396n2 + -2192n2 + 548n3 + (428n3 + -107n4) + -124n4 * (-4 + n) + -2n5 * (-4 + n) + 8n6 * (-4 + n) + n7(-4 + n)) = 0
(2880 + -720n + -1584n + 396n2 + -2192n2 + 548n3 + 428n3 + -107n4 + (-4 * -124n4 + n * -124n4) + -2n5 * (-4 + n) + 8n6 * (-4 + n) + n7(-4 + n)) = 0
(2880 + -720n + -1584n + 396n2 + -2192n2 + 548n3 + 428n3 + -107n4 + (496n4 + -124n5) + -2n5 * (-4 + n) + 8n6 * (-4 + n) + n7(-4 + n)) = 0
(2880 + -720n + -1584n + 396n2 + -2192n2 + 548n3 + 428n3 + -107n4 + 496n4 + -124n5 + (-4 * -2n5 + n * -2n5) + 8n6 * (-4 + n) + n7(-4 + n)) = 0
(2880 + -720n + -1584n + 396n2 + -2192n2 + 548n3 + 428n3 + -107n4 + 496n4 + -124n5 + (8n5 + -2n6) + 8n6 * (-4 + n) + n7(-4 + n)) = 0
(2880 + -720n + -1584n + 396n2 + -2192n2 + 548n3 + 428n3 + -107n4 + 496n4 + -124n5 + 8n5 + -2n6 + (-4 * 8n6 + n * 8n6) + n7(-4 + n)) = 0
(2880 + -720n + -1584n + 396n2 + -2192n2 + 548n3 + 428n3 + -107n4 + 496n4 + -124n5 + 8n5 + -2n6 + (-32n6 + 8n7) + n7(-4 + n)) = 0
(2880 + -720n + -1584n + 396n2 + -2192n2 + 548n3 + 428n3 + -107n4 + 496n4 + -124n5 + 8n5 + -2n6 + -32n6 + 8n7 + (-4 * n7 + n * n7)) = 0
(2880 + -720n + -1584n + 396n2 + -2192n2 + 548n3 + 428n3 + -107n4 + 496n4 + -124n5 + 8n5 + -2n6 + -32n6 + 8n7 + (-4n7 + n8)) = 0

Combine like terms: -720n + -1584n = -2304n
(2880 + -2304n + 396n2 + -2192n2 + 548n3 + 428n3 + -107n4 + 496n4 + -124n5 + 8n5 + -2n6 + -32n6 + 8n7 + -4n7 + n8) = 0

Combine like terms: 396n2 + -2192n2 = -1796n2
(2880 + -2304n + -1796n2 + 548n3 + 428n3 + -107n4 + 496n4 + -124n5 + 8n5 + -2n6 + -32n6 + 8n7 + -4n7 + n8) = 0

Combine like terms: 548n3 + 428n3 = 976n3
(2880 + -2304n + -1796n2 + 976n3 + -107n4 + 496n4 + -124n5 + 8n5 + -2n6 + -32n6 + 8n7 + -4n7 + n8) = 0

Combine like terms: -107n4 + 496n4 = 389n4
(2880 + -2304n + -1796n2 + 976n3 + 389n4 + -124n5 + 8n5 + -2n6 + -32n6 + 8n7 + -4n7 + n8) = 0

Combine like terms: -124n5 + 8n5 = -116n5
(2880 + -2304n + -1796n2 + 976n3 + 389n4 + -116n5 + -2n6 + -32n6 + 8n7 + -4n7 + n8) = 0

Combine like terms: -2n6 + -32n6 = -34n6
(2880 + -2304n + -1796n2 + 976n3 + 389n4 + -116n5 + -34n6 + 8n7 + -4n7 + n8) = 0

Combine like terms: 8n7 + -4n7 = 4n7
(2880 + -2304n + -1796n2 + 976n3 + 389n4 + -116n5 + -34n6 + 4n7 + n8) = 0

Solving
2880 + -2304n + -1796n2 + 976n3 + 389n4 + -116n5 + -34n6 + 4n7 + n8 = 0

Solving for variable 'n'.

The solution to this equation could not be determined.

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