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Simplifying (4 + n)(3 + n)(2 + n)(n + -1)(n + -2)(n + -3)(n + -4) = 0 Reorder the terms: (4 + n)(3 + n)(2 + n)(-1 + n)(n + -2)(n + -3)(n + -4) = 0 Reorder the terms: (4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(n + -3)(n + -4) = 0 Reorder the terms: (4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n)(n + -4) = 0 Reorder the terms: (4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0 Multiply (4 + n) * (3 + n) (4(3 + n) + n(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0 ((3 * 4 + n * 4) + n(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0 ((12 + 4n) + n(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0 (12 + 4n + (3 * n + n * n))(2 + n)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0 (12 + 4n + (3n + n2))(2 + n)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0 Combine like terms: 4n + 3n = 7n (12 + 7n + n2)(2 + n)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0 Multiply (12 + 7n + n2) * (2 + n) (12(2 + n) + 7n * (2 + n) + n2(2 + n))(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0 ((2 * 12 + n * 12) + 7n * (2 + n) + n2(2 + n))(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0 ((24 + 12n) + 7n * (2 + n) + n2(2 + n))(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0 (24 + 12n + (2 * 7n + n * 7n) + n2(2 + n))(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0 (24 + 12n + (14n + 7n2) + n2(2 + n))(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0 (24 + 12n + 14n + 7n2 + (2 * n2 + n * n2))(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0 (24 + 12n + 14n + 7n2 + (2n2 + n3))(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0 Combine like terms: 12n + 14n = 26n (24 + 26n + 7n2 + 2n2 + n3)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0 Combine like terms: 7n2 + 2n2 = 9n2 (24 + 26n + 9n2 + n3)(-1 + n)(-2 + n)(-3 + n)(-4 + n) = 0 Multiply (24 + 26n + 9n2 + n3) * (-1 + n) (24(-1 + n) + 26n * (-1 + n) + 9n2 * (-1 + n) + n3(-1 + n))(-2 + n)(-3 + n)(-4 + n) = 0 ((-1 * 24 + n * 24) + 26n * (-1 + n) + 9n2 * (-1 + n) + n3(-1 + n))(-2 + n)(-3 + n)(-4 + n) = 0 ((-24 + 24n) + 26n * (-1 + n) + 9n2 * (-1 + n) + n3(-1 + n))(-2 + n)(-3 + n)(-4 + n) = 0 (-24 + 24n + (-1 * 26n + n * 26n) + 9n2 * (-1 + n) + n3(-1 + n))(-2 + n)(-3 + n)(-4 + n) = 0 (-24 + 24n + (-26n + 26n2) + 9n2 * (-1 + n) + n3(-1 + n))(-2 + n)(-3 + n)(-4 + n) = 0 (-24 + 24n + -26n + 26n2 + (-1 * 9n2 + n * 9n2) + n3(-1 + n))(-2 + n)(-3 + n)(-4 + n) = 0 (-24 + 24n + -26n + 26n2 + (-9n2 + 9n3) + n3(-1 + n))(-2 + n)(-3 + n)(-4 + n) = 0 (-24 + 24n + -26n + 26n2 + -9n2 + 9n3 + (-1 * n3 + n * n3))(-2 + n)(-3 + n)(-4 + n) = 0 (-24 + 24n + -26n + 26n2 + -9n2 + 9n3 + (-1n3 + n4))(-2 + n)(-3 + n)(-4 + n) = 0 Combine like terms: 24n + -26n = -2n (-24 + -2n + 26n2 + -9n2 + 9n3 + -1n3 + n4)(-2 + n)(-3 + n)(-4 + n) = 0 Combine like terms: 26n2 + -9n2 = 17n2 (-24 + -2n + 17n2 + 9n3 + -1n3 + n4)(-2 + n)(-3 + n)(-4 + n) = 0 Combine like terms: 9n3 + -1n3 = 8n3 (-24 + -2n + 17n2 + 8n3 + n4)(-2 + n)(-3 + n)(-4 + n) = 0 Multiply (-24 + -2n + 17n2 + 8n3 + n4) * (-2 + n) (-24(-2 + n) + -2n * (-2 + n) + 17n2 * (-2 + n) + 8n3 * (-2 + n) + n4(-2 + n))(-3 + n)(-4 + n) = 0 ((-2 * -24 + n * -24) + -2n * (-2 + n) + 17n2 * (-2 + n) + 8n3 * (-2 + n) + n4(-2 + n))(-3 + n)(-4 + n) = 0 ((48 + -24n) + -2n * (-2 + n) + 17n2 * (-2 + n) + 8n3 * (-2 + n) + n4(-2 + n))(-3 + n)(-4 + n) = 0 (48 + -24n + (-2 * -2n + n * -2n) + 17n2 * (-2 + n) + 8n3 * (-2 + n) + n4(-2 + n))(-3 + n)(-4 + n) = 0 (48 + -24n + (4n + -2n2) + 17n2 * (-2 + n) + 8n3 * (-2 + n) + n4(-2 + n))(-3 + n)(-4 + n) = 0 (48 + -24n + 4n + -2n2 + (-2 * 17n2 + n * 17n2) + 8n3 * (-2 + n) + n4(-2 + n))(-3 + n)(-4 + n) = 0 (48 + -24n + 4n + -2n2 + (-34n2 + 17n3) + 8n3 * (-2 + n) + n4(-2 + n))(-3 + n)(-4 + n) = 0 (48 + -24n + 4n + -2n2 + -34n2 + 17n3 + (-2 * 8n3 + n * 8n3) + n4(-2 + n))(-3 + n)(-4 + n) = 0 (48 + -24n + 4n + -2n2 + -34n2 + 17n3 + (-16n3 + 8n4) + n4(-2 + n))(-3 + n)(-4 + n) = 0 (48 + -24n + 4n + -2n2 + -34n2 + 17n3 + -16n3 + 8n4 + (-2 * n4 + n * n4))(-3 + n)(-4 + n) = 0 (48 + -24n + 4n + -2n2 + -34n2 + 17n3 + -16n3 + 8n4 + (-2n4 + n5))(-3 + n)(-4 + n) = 0 Combine like terms: -24n + 4n = -20n (48 + -20n + -2n2 + -34n2 + 17n3 + -16n3 + 8n4 + -2n4 + n5)(-3 + n)(-4 + n) = 0 Combine like terms: -2n2 + -34n2 = -36n2 (48 + -20n + -36n2 + 17n3 + -16n3 + 8n4 + -2n4 + n5)(-3 + n)(-4 + n) = 0 Combine like terms: 17n3 + -16n3 = 1n3 (48 + -20n + -36n2 + 1n3 + 8n4 + -2n4 + n5)(-3 + n)(-4 + n) = 0 Combine like terms: 8n4 + -2n4 = 6n4 (48 + -20n + -36n2 + 1n3 + 6n4 + n5)(-3 + n)(-4 + n) = 0 Multiply (48 + -20n + -36n2 + 1n3 + 6n4 + n5) * (-3 + n) (48(-3 + n) + -20n * (-3 + n) + -36n2 * (-3 + n) + 1n3 * (-3 + n) + 6n4 * (-3 + n) + n5(-3 + n))(-4 + n) = 0 ((-3 * 48 + n * 48) + -20n * (-3 + n) + -36n2 * (-3 + n) + 1n3 * (-3 + n) + 6n4 * (-3 + n) + n5(-3 + n))(-4 + n) = 0 ((-144 + 48n) + -20n * (-3 + n) + -36n2 * (-3 + n) + 1n3 * (-3 + n) + 6n4 * (-3 + n) + n5(-3 + n))(-4 + n) = 0 (-144 + 48n + (-3 * -20n + n * -20n) + -36n2 * (-3 + n) + 1n3 * (-3 + n) + 6n4 * (-3 + n) + n5(-3 + n))(-4 + n) = 0 (-144 + 48n + (60n + -20n2) + -36n2 * (-3 + n) + 1n3 * (-3 + n) + 6n4 * (-3 + n) + n5(-3 + n))(-4 + n) = 0 (-144 + 48n + 60n + -20n2 + (-3 * -36n2 + n * -36n2) + 1n3 * (-3 + n) + 6n4 * (-3 + n) + n5(-3 + n))(-4 + n) = 0 (-144 + 48n + 60n + -20n2 + (108n2 + -36n3) + 1n3 * (-3 + n) + 6n4 * (-3 + n) + n5(-3 + n))(-4 + n) = 0 (-144 + 48n + 60n + -20n2 + 108n2 + -36n3 + (-3 * 1n3 + n * 1n3) + 6n4 * (-3 + n) + n5(-3 + n))(-4 + n) = 0 (-144 + 48n + 60n + -20n2 + 108n2 + -36n3 + (-3n3 + 1n4) + 6n4 * (-3 + n) + n5(-3 + n))(-4 + n) = 0 (-144 + 48n + 60n + -20n2 + 108n2 + -36n3 + -3n3 + 1n4 + (-3 * 6n4 + n * 6n4) + n5(-3 + n))(-4 + n) = 0 (-144 + 48n + 60n + -20n2 + 108n2 + -36n3 + -3n3 + 1n4 + (-18n4 + 6n5) + n5(-3 + n))(-4 + n) = 0 (-144 + 48n + 60n + -20n2 + 108n2 + -36n3 + -3n3 + 1n4 + -18n4 + 6n5 + (-3 * n5 + n * n5))(-4 + n) = 0 (-144 + 48n + 60n + -20n2 + 108n2 + -36n3 + -3n3 + 1n4 + -18n4 + 6n5 + (-3n5 + n6))(-4 + n) = 0 Combine like terms: 48n + 60n = 108n (-144 + 108n + -20n2 + 108n2 + -36n3 + -3n3 + 1n4 + -18n4 + 6n5 + -3n5 + n6)(-4 + n) = 0 Combine like terms: -20n2 + 108n2 = 88n2 (-144 + 108n + 88n2 + -36n3 + -3n3 + 1n4 + -18n4 + 6n5 + -3n5 + n6)(-4 + n) = 0 Combine like terms: -36n3 + -3n3 = -39n3 (-144 + 108n + 88n2 + -39n3 + 1n4 + -18n4 + 6n5 + -3n5 + n6)(-4 + n) = 0 Combine like terms: 1n4 + -18n4 = -17n4 (-144 + 108n + 88n2 + -39n3 + -17n4 + 6n5 + -3n5 + n6)(-4 + n) = 0 Combine like terms: 6n5 + -3n5 = 3n5 (-144 + 108n + 88n2 + -39n3 + -17n4 + 3n5 + n6)(-4 + n) = 0 Multiply (-144 + 108n + 88n2 + -39n3 + -17n4 + 3n5 + n6) * (-4 + n) (-144(-4 + n) + 108n * (-4 + n) + 88n2 * (-4 + n) + -39n3 * (-4 + n) + -17n4 * (-4 + n) + 3n5 * (-4 + n) + n6(-4 + n)) = 0 ((-4 * -144 + n * -144) + 108n * (-4 + n) + 88n2 * (-4 + n) + -39n3 * (-4 + n) + -17n4 * (-4 + n) + 3n5 * (-4 + n) + n6(-4 + n)) = 0 ((576 + -144n) + 108n * (-4 + n) + 88n2 * (-4 + n) + -39n3 * (-4 + n) + -17n4 * (-4 + n) + 3n5 * (-4 + n) + n6(-4 + n)) = 0 (576 + -144n + (-4 * 108n + n * 108n) + 88n2 * (-4 + n) + -39n3 * (-4 + n) + -17n4 * (-4 + n) + 3n5 * (-4 + n) + n6(-4 + n)) = 0 (576 + -144n + (-432n + 108n2) + 88n2 * (-4 + n) + -39n3 * (-4 + n) + -17n4 * (-4 + n) + 3n5 * (-4 + n) + n6(-4 + n)) = 0 (576 + -144n + -432n + 108n2 + (-4 * 88n2 + n * 88n2) + -39n3 * (-4 + n) + -17n4 * (-4 + n) + 3n5 * (-4 + n) + n6(-4 + n)) = 0 (576 + -144n + -432n + 108n2 + (-352n2 + 88n3) + -39n3 * (-4 + n) + -17n4 * (-4 + n) + 3n5 * (-4 + n) + n6(-4 + n)) = 0 (576 + -144n + -432n + 108n2 + -352n2 + 88n3 + (-4 * -39n3 + n * -39n3) + -17n4 * (-4 + n) + 3n5 * (-4 + n) + n6(-4 + n)) = 0 (576 + -144n + -432n + 108n2 + -352n2 + 88n3 + (156n3 + -39n4) + -17n4 * (-4 + n) + 3n5 * (-4 + n) + n6(-4 + n)) = 0 (576 + -144n + -432n + 108n2 + -352n2 + 88n3 + 156n3 + -39n4 + (-4 * -17n4 + n * -17n4) + 3n5 * (-4 + n) + n6(-4 + n)) = 0 (576 + -144n + -432n + 108n2 + -352n2 + 88n3 + 156n3 + -39n4 + (68n4 + -17n5) + 3n5 * (-4 + n) + n6(-4 + n)) = 0 (576 + -144n + -432n + 108n2 + -352n2 + 88n3 + 156n3 + -39n4 + 68n4 + -17n5 + (-4 * 3n5 + n * 3n5) + n6(-4 + n)) = 0 (576 + -144n + -432n + 108n2 + -352n2 + 88n3 + 156n3 + -39n4 + 68n4 + -17n5 + (-12n5 + 3n6) + n6(-4 + n)) = 0 (576 + -144n + -432n + 108n2 + -352n2 + 88n3 + 156n3 + -39n4 + 68n4 + -17n5 + -12n5 + 3n6 + (-4 * n6 + n * n6)) = 0 (576 + -144n + -432n + 108n2 + -352n2 + 88n3 + 156n3 + -39n4 + 68n4 + -17n5 + -12n5 + 3n6 + (-4n6 + n7)) = 0 Combine like terms: -144n + -432n = -576n (576 + -576n + 108n2 + -352n2 + 88n3 + 156n3 + -39n4 + 68n4 + -17n5 + -12n5 + 3n6 + -4n6 + n7) = 0 Combine like terms: 108n2 + -352n2 = -244n2 (576 + -576n + -244n2 + 88n3 + 156n3 + -39n4 + 68n4 + -17n5 + -12n5 + 3n6 + -4n6 + n7) = 0 Combine like terms: 88n3 + 156n3 = 244n3 (576 + -576n + -244n2 + 244n3 + -39n4 + 68n4 + -17n5 + -12n5 + 3n6 + -4n6 + n7) = 0 Combine like terms: -39n4 + 68n4 = 29n4 (576 + -576n + -244n2 + 244n3 + 29n4 + -17n5 + -12n5 + 3n6 + -4n6 + n7) = 0 Combine like terms: -17n5 + -12n5 = -29n5 (576 + -576n + -244n2 + 244n3 + 29n4 + -29n5 + 3n6 + -4n6 + n7) = 0 Combine like terms: 3n6 + -4n6 = -1n6 (576 + -576n + -244n2 + 244n3 + 29n4 + -29n5 + -1n6 + n7) = 0 Solving 576 + -576n + -244n2 + 244n3 + 29n4 + -29n5 + -1n6 + n7 = 0 Solving for variable 'n'. The solution to this equation could not be determined.
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