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Simplifying (n + -4)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(n + -1)(n + -2)(n + -3) = 0 Reorder the terms: (-4 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(n + -1)(n + -2)(n + -3) = 0 Reorder the terms: (-4 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(n + -2)(n + -3) = 0 Reorder the terms: (-4 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(n + -3) = 0 Reorder the terms: (-4 + n)(7 + n)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Multiply (-4 + n) * (7 + n) (-4(7 + n) + n(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((7 * -4 + n * -4) + n(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((-28 + -4n) + n(7 + n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-28 + -4n + (7 * n + n * n))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-28 + -4n + (7n + n2))(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: -4n + 7n = 3n (-28 + 3n + n2)(6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Multiply (-28 + 3n + n2) * (6 + n) (-28(6 + n) + 3n * (6 + n) + n2(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((6 * -28 + n * -28) + 3n * (6 + n) + n2(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((-168 + -28n) + 3n * (6 + n) + n2(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-168 + -28n + (6 * 3n + n * 3n) + n2(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-168 + -28n + (18n + 3n2) + n2(6 + n))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-168 + -28n + 18n + 3n2 + (6 * n2 + n * n2))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-168 + -28n + 18n + 3n2 + (6n2 + n3))(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: -28n + 18n = -10n (-168 + -10n + 3n2 + 6n2 + n3)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 3n2 + 6n2 = 9n2 (-168 + -10n + 9n2 + n3)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Multiply (-168 + -10n + 9n2 + n3) * (5 + n) (-168(5 + n) + -10n * (5 + n) + 9n2 * (5 + n) + n3(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((5 * -168 + n * -168) + -10n * (5 + n) + 9n2 * (5 + n) + n3(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((-840 + -168n) + -10n * (5 + n) + 9n2 * (5 + n) + n3(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-840 + -168n + (5 * -10n + n * -10n) + 9n2 * (5 + n) + n3(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-840 + -168n + (-50n + -10n2) + 9n2 * (5 + n) + n3(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-840 + -168n + -50n + -10n2 + (5 * 9n2 + n * 9n2) + n3(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-840 + -168n + -50n + -10n2 + (45n2 + 9n3) + n3(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-840 + -168n + -50n + -10n2 + 45n2 + 9n3 + (5 * n3 + n * n3))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-840 + -168n + -50n + -10n2 + 45n2 + 9n3 + (5n3 + n4))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: -168n + -50n = -218n (-840 + -218n + -10n2 + 45n2 + 9n3 + 5n3 + n4)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: -10n2 + 45n2 = 35n2 (-840 + -218n + 35n2 + 9n3 + 5n3 + n4)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 9n3 + 5n3 = 14n3 (-840 + -218n + 35n2 + 14n3 + n4)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Multiply (-840 + -218n + 35n2 + 14n3 + n4) * (4 + n) (-840(4 + n) + -218n * (4 + n) + 35n2 * (4 + n) + 14n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((4 * -840 + n * -840) + -218n * (4 + n) + 35n2 * (4 + n) + 14n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((-3360 + -840n) + -218n * (4 + n) + 35n2 * (4 + n) + 14n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-3360 + -840n + (4 * -218n + n * -218n) + 35n2 * (4 + n) + 14n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-3360 + -840n + (-872n + -218n2) + 35n2 * (4 + n) + 14n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-3360 + -840n + -872n + -218n2 + (4 * 35n2 + n * 35n2) + 14n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-3360 + -840n + -872n + -218n2 + (140n2 + 35n3) + 14n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-3360 + -840n + -872n + -218n2 + 140n2 + 35n3 + (4 * 14n3 + n * 14n3) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-3360 + -840n + -872n + -218n2 + 140n2 + 35n3 + (56n3 + 14n4) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-3360 + -840n + -872n + -218n2 + 140n2 + 35n3 + 56n3 + 14n4 + (4 * n4 + n * n4))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-3360 + -840n + -872n + -218n2 + 140n2 + 35n3 + 56n3 + 14n4 + (4n4 + n5))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: -840n + -872n = -1712n (-3360 + -1712n + -218n2 + 140n2 + 35n3 + 56n3 + 14n4 + 4n4 + n5)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: -218n2 + 140n2 = -78n2 (-3360 + -1712n + -78n2 + 35n3 + 56n3 + 14n4 + 4n4 + n5)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 35n3 + 56n3 = 91n3 (-3360 + -1712n + -78n2 + 91n3 + 14n4 + 4n4 + n5)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 14n4 + 4n4 = 18n4 (-3360 + -1712n + -78n2 + 91n3 + 18n4 + n5)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Multiply (-3360 + -1712n + -78n2 + 91n3 + 18n4 + n5) * (3 + n) (-3360(3 + n) + -1712n * (3 + n) + -78n2 * (3 + n) + 91n3 * (3 + n) + 18n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((3 * -3360 + n * -3360) + -1712n * (3 + n) + -78n2 * (3 + n) + 91n3 * (3 + n) + 18n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((-10080 + -3360n) + -1712n * (3 + n) + -78n2 * (3 + n) + 91n3 * (3 + n) + 18n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-10080 + -3360n + (3 * -1712n + n * -1712n) + -78n2 * (3 + n) + 91n3 * (3 + n) + 18n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-10080 + -3360n + (-5136n + -1712n2) + -78n2 * (3 + n) + 91n3 * (3 + n) + 18n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-10080 + -3360n + -5136n + -1712n2 + (3 * -78n2 + n * -78n2) + 91n3 * (3 + n) + 18n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-10080 + -3360n + -5136n + -1712n2 + (-234n2 + -78n3) + 91n3 * (3 + n) + 18n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-10080 + -3360n + -5136n + -1712n2 + -234n2 + -78n3 + (3 * 91n3 + n * 91n3) + 18n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-10080 + -3360n + -5136n + -1712n2 + -234n2 + -78n3 + (273n3 + 91n4) + 18n4 * (3 + n) + n5(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-10080 + -3360n + -5136n + -1712n2 + -234n2 + -78n3 + 273n3 + 91n4 + (3 * 18n4 + n * 18n4) + n5(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-10080 + -3360n + -5136n + -1712n2 + -234n2 + -78n3 + 273n3 + 91n4 + (54n4 + 18n5) + n5(3 + n))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-10080 + -3360n + -5136n + -1712n2 + -234n2 + -78n3 + 273n3 + 91n4 + 54n4 + 18n5 + (3 * n5 + n * n5))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-10080 + -3360n + -5136n + -1712n2 + -234n2 + -78n3 + 273n3 + 91n4 + 54n4 + 18n5 + (3n5 + n6))(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: -3360n + -5136n = -8496n (-10080 + -8496n + -1712n2 + -234n2 + -78n3 + 273n3 + 91n4 + 54n4 + 18n5 + 3n5 + n6)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: -1712n2 + -234n2 = -1946n2 (-10080 + -8496n + -1946n2 + -78n3 + 273n3 + 91n4 + 54n4 + 18n5 + 3n5 + n6)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: -78n3 + 273n3 = 195n3 (-10080 + -8496n + -1946n2 + 195n3 + 91n4 + 54n4 + 18n5 + 3n5 + n6)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 91n4 + 54n4 = 145n4 (-10080 + -8496n + -1946n2 + 195n3 + 145n4 + 18n5 + 3n5 + n6)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 18n5 + 3n5 = 21n5 (-10080 + -8496n + -1946n2 + 195n3 + 145n4 + 21n5 + n6)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Multiply (-10080 + -8496n + -1946n2 + 195n3 + 145n4 + 21n5 + n6) * (2 + n) (-10080(2 + n) + -8496n * (2 + n) + -1946n2 * (2 + n) + 195n3 * (2 + n) + 145n4 * (2 + n) + 21n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 ((2 * -10080 + n * -10080) + -8496n * (2 + n) + -1946n2 * (2 + n) + 195n3 * (2 + n) + 145n4 * (2 + n) + 21n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 ((-20160 + -10080n) + -8496n * (2 + n) + -1946n2 * (2 + n) + 195n3 * (2 + n) + 145n4 * (2 + n) + 21n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (-20160 + -10080n + (2 * -8496n + n * -8496n) + -1946n2 * (2 + n) + 195n3 * (2 + n) + 145n4 * (2 + n) + 21n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (-20160 + -10080n + (-16992n + -8496n2) + -1946n2 * (2 + n) + 195n3 * (2 + n) + 145n4 * (2 + n) + 21n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (-20160 + -10080n + -16992n + -8496n2 + (2 * -1946n2 + n * -1946n2) + 195n3 * (2 + n) + 145n4 * (2 + n) + 21n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (-20160 + -10080n + -16992n + -8496n2 + (-3892n2 + -1946n3) + 195n3 * (2 + n) + 145n4 * (2 + n) + 21n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (-20160 + -10080n + -16992n + -8496n2 + -3892n2 + -1946n3 + (2 * 195n3 + n * 195n3) + 145n4 * (2 + n) + 21n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (-20160 + -10080n + -16992n + -8496n2 + -3892n2 + -1946n3 + (390n3 + 195n4) + 145n4 * (2 + n) + 21n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (-20160 + -10080n + -16992n + -8496n2 + -3892n2 + -1946n3 + 390n3 + 195n4 + (2 * 145n4 + n * 145n4) + 21n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (-20160 + -10080n + -16992n + -8496n2 + -3892n2 + -1946n3 + 390n3 + 195n4 + (290n4 + 145n5) + 21n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (-20160 + -10080n + -16992n + -8496n2 + -3892n2 + -1946n3 + 390n3 + 195n4 + 290n4 + 145n5 + (2 * 21n5 + n * 21n5) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (-20160 + -10080n + -16992n + -8496n2 + -3892n2 + -1946n3 + 390n3 + 195n4 + 290n4 + 145n5 + (42n5 + 21n6) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (-20160 + -10080n + -16992n + -8496n2 + -3892n2 + -1946n3 + 390n3 + 195n4 + 290n4 + 145n5 + 42n5 + 21n6 + (2 * n6 + n * n6))(-1 + n)(-2 + n)(-3 + n) = 0 (-20160 + -10080n + -16992n + -8496n2 + -3892n2 + -1946n3 + 390n3 + 195n4 + 290n4 + 145n5 + 42n5 + 21n6 + (2n6 + n7))(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: -10080n + -16992n = -27072n (-20160 + -27072n + -8496n2 + -3892n2 + -1946n3 + 390n3 + 195n4 + 290n4 + 145n5 + 42n5 + 21n6 + 2n6 + n7)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: -8496n2 + -3892n2 = -12388n2 (-20160 + -27072n + -12388n2 + -1946n3 + 390n3 + 195n4 + 290n4 + 145n5 + 42n5 + 21n6 + 2n6 + n7)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: -1946n3 + 390n3 = -1556n3 (-20160 + -27072n + -12388n2 + -1556n3 + 195n4 + 290n4 + 145n5 + 42n5 + 21n6 + 2n6 + n7)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 195n4 + 290n4 = 485n4 (-20160 + -27072n + -12388n2 + -1556n3 + 485n4 + 145n5 + 42n5 + 21n6 + 2n6 + n7)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 145n5 + 42n5 = 187n5 (-20160 + -27072n + -12388n2 + -1556n3 + 485n4 + 187n5 + 21n6 + 2n6 + n7)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 21n6 + 2n6 = 23n6 (-20160 + -27072n + -12388n2 + -1556n3 + 485n4 + 187n5 + 23n6 + n7)(-1 + n)(-2 + n)(-3 + n) = 0 Multiply (-20160 + -27072n + -12388n2 + -1556n3 + 485n4 + 187n5 + 23n6 + n7) * (-1 + n) (-20160(-1 + n) + -27072n * (-1 + n) + -12388n2 * (-1 + n) + -1556n3 * (-1 + n) + 485n4 * (-1 + n) + 187n5 * (-1 + n) + 23n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 ((-1 * -20160 + n * -20160) + -27072n * (-1 + n) + -12388n2 * (-1 + n) + -1556n3 * (-1 + n) + 485n4 * (-1 + n) + 187n5 * (-1 + n) + 23n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 ((20160 + -20160n) + -27072n * (-1 + n) + -12388n2 * (-1 + n) + -1556n3 * (-1 + n) + 485n4 * (-1 + n) + 187n5 * (-1 + n) + 23n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (20160 + -20160n + (-1 * -27072n + n * -27072n) + -12388n2 * (-1 + n) + -1556n3 * (-1 + n) + 485n4 * (-1 + n) + 187n5 * (-1 + n) + 23n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (20160 + -20160n + (27072n + -27072n2) + -12388n2 * (-1 + n) + -1556n3 * (-1 + n) + 485n4 * (-1 + n) + 187n5 * (-1 + n) + 23n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (20160 + -20160n + 27072n + -27072n2 + (-1 * -12388n2 + n * -12388n2) + -1556n3 * (-1 + n) + 485n4 * (-1 + n) + 187n5 * (-1 + n) + 23n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (20160 + -20160n + 27072n + -27072n2 + (12388n2 + -12388n3) + -1556n3 * (-1 + n) + 485n4 * (-1 + n) + 187n5 * (-1 + n) + 23n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (20160 + -20160n + 27072n + -27072n2 + 12388n2 + -12388n3 + (-1 * -1556n3 + n * -1556n3) + 485n4 * (-1 + n) + 187n5 * (-1 + n) + 23n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (20160 + -20160n + 27072n + -27072n2 + 12388n2 + -12388n3 + (1556n3 + -1556n4) + 485n4 * (-1 + n) + 187n5 * (-1 + n) + 23n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (20160 + -20160n + 27072n + -27072n2 + 12388n2 + -12388n3 + 1556n3 + -1556n4 + (-1 * 485n4 + n * 485n4) + 187n5 * (-1 + n) + 23n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (20160 + -20160n + 27072n + -27072n2 + 12388n2 + -12388n3 + 1556n3 + -1556n4 + (-485n4 + 485n5) + 187n5 * (-1 + n) + 23n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (20160 + -20160n + 27072n + -27072n2 + 12388n2 + -12388n3 + 1556n3 + -1556n4 + -485n4 + 485n5 + (-1 * 187n5 + n * 187n5) + 23n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (20160 + -20160n + 27072n + -27072n2 + 12388n2 + -12388n3 + 1556n3 + -1556n4 + -485n4 + 485n5 + (-187n5 + 187n6) + 23n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (20160 + -20160n + 27072n + -27072n2 + 12388n2 + -12388n3 + 1556n3 + -1556n4 + -485n4 + 485n5 + -187n5 + 187n6 + (-1 * 23n6 + n * 23n6) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (20160 + -20160n + 27072n + -27072n2 + 12388n2 + -12388n3 + 1556n3 + -1556n4 + -485n4 + 485n5 + -187n5 + 187n6 + (-23n6 + 23n7) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (20160 + -20160n + 27072n + -27072n2 + 12388n2 + -12388n3 + 1556n3 + -1556n4 + -485n4 + 485n5 + -187n5 + 187n6 + -23n6 + 23n7 + (-1 * n7 + n * n7))(-2 + n)(-3 + n) = 0 (20160 + -20160n + 27072n + -27072n2 + 12388n2 + -12388n3 + 1556n3 + -1556n4 + -485n4 + 485n5 + -187n5 + 187n6 + -23n6 + 23n7 + (-1n7 + n8))(-2 + n)(-3 + n) = 0 Combine like terms: -20160n + 27072n = 6912n (20160 + 6912n + -27072n2 + 12388n2 + -12388n3 + 1556n3 + -1556n4 + -485n4 + 485n5 + -187n5 + 187n6 + -23n6 + 23n7 + -1n7 + n8)(-2 + n)(-3 + n) = 0 Combine like terms: -27072n2 + 12388n2 = -14684n2 (20160 + 6912n + -14684n2 + -12388n3 + 1556n3 + -1556n4 + -485n4 + 485n5 + -187n5 + 187n6 + -23n6 + 23n7 + -1n7 + n8)(-2 + n)(-3 + n) = 0 Combine like terms: -12388n3 + 1556n3 = -10832n3 (20160 + 6912n + -14684n2 + -10832n3 + -1556n4 + -485n4 + 485n5 + -187n5 + 187n6 + -23n6 + 23n7 + -1n7 + n8)(-2 + n)(-3 + n) = 0 Combine like terms: -1556n4 + -485n4 = -2041n4 (20160 + 6912n + -14684n2 + -10832n3 + -2041n4 + 485n5 + -187n5 + 187n6 + -23n6 + 23n7 + -1n7 + n8)(-2 + n)(-3 + n) = 0 Combine like terms: 485n5 + -187n5 = 298n5 (20160 + 6912n + -14684n2 + -10832n3 + -2041n4 + 298n5 + 187n6 + -23n6 + 23n7 + -1n7 + n8)(-2 + n)(-3 + n) = 0 Combine like terms: 187n6 + -23n6 = 164n6 (20160 + 6912n + -14684n2 + -10832n3 + -2041n4 + 298n5 + 164n6 + 23n7 + -1n7 + n8)(-2 + n)(-3 + n) = 0 Combine like terms: 23n7 + -1n7 = 22n7 (20160 + 6912n + -14684n2 + -10832n3 + -2041n4 + 298n5 + 164n6 + 22n7 + n8)(-2 + n)(-3 + n) = 0 Multiply (20160 + 6912n + -14684n2 + -10832n3 + -2041n4 + 298n5 + 164n6 + 22n7 + n8) * (-2 + n) (20160(-2 + n) + 6912n * (-2 + n) + -14684n2 * (-2 + n) + -10832n3 * (-2 + n) + -2041n4 * (-2 + n) + 298n5 * (-2 + n) + 164n6 * (-2 + n) + 22n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 ((-2 * 20160 + n * 20160) + 6912n * (-2 + n) + -14684n2 * (-2 + n) + -10832n3 * (-2 + n) + -2041n4 * (-2 + n) + 298n5 * (-2 + n) + 164n6 * (-2 + n) + 22n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 ((-40320 + 20160n) + 6912n * (-2 + n) + -14684n2 * (-2 + n) + -10832n3 * (-2 + n) + -2041n4 * (-2 + n) + 298n5 * (-2 + n) + 164n6 * (-2 + n) + 22n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (-40320 + 20160n + (-2 * 6912n + n * 6912n) + -14684n2 * (-2 + n) + -10832n3 * (-2 + n) + -2041n4 * (-2 + n) + 298n5 * (-2 + n) + 164n6 * (-2 + n) + 22n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (-40320 + 20160n + (-13824n + 6912n2) + -14684n2 * (-2 + n) + -10832n3 * (-2 + n) + -2041n4 * (-2 + n) + 298n5 * (-2 + n) + 164n6 * (-2 + n) + 22n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (-40320 + 20160n + -13824n + 6912n2 + (-2 * -14684n2 + n * -14684n2) + -10832n3 * (-2 + n) + -2041n4 * (-2 + n) + 298n5 * (-2 + n) + 164n6 * (-2 + n) + 22n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (-40320 + 20160n + -13824n + 6912n2 + (29368n2 + -14684n3) + -10832n3 * (-2 + n) + -2041n4 * (-2 + n) + 298n5 * (-2 + n) + 164n6 * (-2 + n) + 22n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (-40320 + 20160n + -13824n + 6912n2 + 29368n2 + -14684n3 + (-2 * -10832n3 + n * -10832n3) + -2041n4 * (-2 + n) + 298n5 * (-2 + n) + 164n6 * (-2 + n) + 22n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (-40320 + 20160n + -13824n + 6912n2 + 29368n2 + -14684n3 + (21664n3 + -10832n4) + -2041n4 * (-2 + n) + 298n5 * (-2 + n) + 164n6 * (-2 + n) + 22n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (-40320 + 20160n + -13824n + 6912n2 + 29368n2 + -14684n3 + 21664n3 + -10832n4 + (-2 * -2041n4 + n * -2041n4) + 298n5 * (-2 + n) + 164n6 * (-2 + n) + 22n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (-40320 + 20160n + -13824n + 6912n2 + 29368n2 + -14684n3 + 21664n3 + -10832n4 + (4082n4 + -2041n5) + 298n5 * (-2 + n) + 164n6 * (-2 + n) + 22n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (-40320 + 20160n + -13824n + 6912n2 + 29368n2 + -14684n3 + 21664n3 + -10832n4 + 4082n4 + -2041n5 + (-2 * 298n5 + n * 298n5) + 164n6 * (-2 + n) + 22n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (-40320 + 20160n + -13824n + 6912n2 + 29368n2 + -14684n3 + 21664n3 + -10832n4 + 4082n4 + -2041n5 + (-596n5 + 298n6) + 164n6 * (-2 + n) + 22n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (-40320 + 20160n + -13824n + 6912n2 + 29368n2 + -14684n3 + 21664n3 + -10832n4 + 4082n4 + -2041n5 + -596n5 + 298n6 + (-2 * 164n6 + n * 164n6) + 22n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (-40320 + 20160n + -13824n + 6912n2 + 29368n2 + -14684n3 + 21664n3 + -10832n4 + 4082n4 + -2041n5 + -596n5 + 298n6 + (-328n6 + 164n7) + 22n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (-40320 + 20160n + -13824n + 6912n2 + 29368n2 + -14684n3 + 21664n3 + -10832n4 + 4082n4 + -2041n5 + -596n5 + 298n6 + -328n6 + 164n7 + (-2 * 22n7 + n * 22n7) + n8(-2 + n))(-3 + n) = 0 (-40320 + 20160n + -13824n + 6912n2 + 29368n2 + -14684n3 + 21664n3 + -10832n4 + 4082n4 + -2041n5 + -596n5 + 298n6 + -328n6 + 164n7 + (-44n7 + 22n8) + n8(-2 + n))(-3 + n) = 0 (-40320 + 20160n + -13824n + 6912n2 + 29368n2 + -14684n3 + 21664n3 + -10832n4 + 4082n4 + -2041n5 + -596n5 + 298n6 + -328n6 + 164n7 + -44n7 + 22n8 + (-2 * n8 + n * n8))(-3 + n) = 0 (-40320 + 20160n + -13824n + 6912n2 + 29368n2 + -14684n3 + 21664n3 + -10832n4 + 4082n4 + -2041n5 + -596n5 + 298n6 + -328n6 + 164n7 + -44n7 + 22n8 + (-2n8 + n9))(-3 + n) = 0 Combine like terms: 20160n + -13824n = 6336n (-40320 + 6336n + 6912n2 + 29368n2 + -14684n3 + 21664n3 + -10832n4 + 4082n4 + -2041n5 + -596n5 + 298n6 + -328n6 + 164n7 + -44n7 + 22n8 + -2n8 + n9)(-3 + n) = 0 Combine like terms: 6912n2 + 29368n2 = 36280n2 (-40320 + 6336n + 36280n2 + -14684n3 + 21664n3 + -10832n4 + 4082n4 + -2041n5 + -596n5 + 298n6 + -328n6 + 164n7 + -44n7 + 22n8 + -2n8 + n9)(-3 + n) = 0 Combine like terms: -14684n3 + 21664n3 = 6980n3 (-40320 + 6336n + 36280n2 + 6980n3 + -10832n4 + 4082n4 + -2041n5 + -596n5 + 298n6 + -328n6 + 164n7 + -44n7 + 22n8 + -2n8 + n9)(-3 + n) = 0 Combine like terms: -10832n4 + 4082n4 = -6750n4 (-40320 + 6336n + 36280n2 + 6980n3 + -6750n4 + -2041n5 + -596n5 + 298n6 + -328n6 + 164n7 + -44n7 + 22n8 + -2n8 + n9)(-3 + n) = 0 Combine like terms: -2041n5 + -596n5 = -2637n5 (-40320 + 6336n + 36280n2 + 6980n3 + -6750n4 + -2637n5 + 298n6 + -328n6 + 164n7 + -44n7 + 22n8 + -2n8 + n9)(-3 + n) = 0 Combine like terms: 298n6 + -328n6 = -30n6 (-40320 + 6336n + 36280n2 + 6980n3 + -6750n4 + -2637n5 + -30n6 + 164n7 + -44n7 + 22n8 + -2n8 + n9)(-3 + n) = 0 Combine like terms: 164n7 + -44n7 = 120n7 (-40320 + 6336n + 36280n2 + 6980n3 + -6750n4 + -2637n5 + -30n6 + 120n7 + 22n8 + -2n8 + n9)(-3 + n) = 0 Combine like terms: 22n8 + -2n8 = 20n8 (-40320 + 6336n + 36280n2 + 6980n3 + -6750n4 + -2637n5 + -30n6 + 120n7 + 20n8 + n9)(-3 + n) = 0 Multiply (-40320 + 6336n + 36280n2 + 6980n3 + -6750n4 + -2637n5 + -30n6 + 120n7 + 20n8 + n9) * (-3 + n) (-40320(-3 + n) + 6336n * (-3 + n) + 36280n2 * (-3 + n) + 6980n3 * (-3 + n) + -6750n4 * (-3 + n) + -2637n5 * (-3 + n) + -30n6 * (-3 + n) + 120n7 * (-3 + n) + 20n8 * (-3 + n) + n9(-3 + n)) = 0 ((-3 * -40320 + n * -40320) + 6336n * (-3 + n) + 36280n2 * (-3 + n) + 6980n3 * (-3 + n) + -6750n4 * (-3 + n) + -2637n5 * (-3 + n) + -30n6 * (-3 + n) + 120n7 * (-3 + n) + 20n8 * (-3 + n) + n9(-3 + n)) = 0 ((120960 + -40320n) + 6336n * (-3 + n) + 36280n2 * (-3 + n) + 6980n3 * (-3 + n) + -6750n4 * (-3 + n) + -2637n5 * (-3 + n) + -30n6 * (-3 + n) + 120n7 * (-3 + n) + 20n8 * (-3 + n) + n9(-3 + n)) = 0 (120960 + -40320n + (-3 * 6336n + n * 6336n) + 36280n2 * (-3 + n) + 6980n3 * (-3 + n) + -6750n4 * (-3 + n) + -2637n5 * (-3 + n) + -30n6 * (-3 + n) + 120n7 * (-3 + n) + 20n8 * (-3 + n) + n9(-3 + n)) = 0 (120960 + -40320n + (-19008n + 6336n2) + 36280n2 * (-3 + n) + 6980n3 * (-3 + n) + -6750n4 * (-3 + n) + -2637n5 * (-3 + n) + -30n6 * (-3 + n) + 120n7 * (-3 + n) + 20n8 * (-3 + n) + n9(-3 + n)) = 0 (120960 + -40320n + -19008n + 6336n2 + (-3 * 36280n2 + n * 36280n2) + 6980n3 * (-3 + n) + -6750n4 * (-3 + n) + -2637n5 * (-3 + n) + -30n6 * (-3 + n) + 120n7 * (-3 + n) + 20n8 * (-3 + n) + n9(-3 + n)) = 0 (120960 + -40320n + -19008n + 6336n2 + (-108840n2 + 36280n3) + 6980n3 * (-3 + n) + -6750n4 * (-3 + n) + -2637n5 * (-3 + n) + -30n6 * (-3 + n) + 120n7 * (-3 + n) + 20n8 * (-3 + n) + n9(-3 + n)) = 0 (120960 + -40320n + -19008n + 6336n2 + -108840n2 + 36280n3 + (-3 * 6980n3 + n * 6980n3) + -6750n4 * (-3 + n) + -2637n5 * (-3 + n) + -30n6 * (-3 + n) + 120n7 * (-3 + n) + 20n8 * (-3 + n) + n9(-3 + n)) = 0 (120960 + -40320n + -19008n + 6336n2 + -108840n2 + 36280n3 + (-20940n3 + 6980n4) + -6750n4 * (-3 + n) + -2637n5 * (-3 + n) + -30n6 * (-3 + n) + 120n7 * (-3 + n) + 20n8 * (-3 + n) + n9(-3 + n)) = 0 (120960 + -40320n + -19008n + 6336n2 + -108840n2 + 36280n3 + -20940n3 + 6980n4 + (-3 * -6750n4 + n * -6750n4) + -2637n5 * (-3 + n) + -30n6 * (-3 + n) + 120n7 * (-3 + n) + 20n8 * (-3 + n) + n9(-3 + n)) = 0 (120960 + -40320n + -19008n + 6336n2 + -108840n2 + 36280n3 + -20940n3 + 6980n4 + (20250n4 + -6750n5) + -2637n5 * (-3 + n) + -30n6 * (-3 + n) + 120n7 * (-3 + n) + 20n8 * (-3 + n) + n9(-3 + n)) = 0 (120960 + -40320n + -19008n + 6336n2 + -108840n2 + 36280n3 + -20940n3 + 6980n4 + 20250n4 + -6750n5 + (-3 * -2637n5 + n * -2637n5) + -30n6 * (-3 + n) + 120n7 * (-3 + n) + 20n8 * (-3 + n) + n9(-3 + n)) = 0 (120960 + -40320n + -19008n + 6336n2 + -108840n2 + 36280n3 + -20940n3 + 6980n4 + 20250n4 + -6750n5 + (7911n5 + -2637n6) + -30n6 * (-3 + n) + 120n7 * (-3 + n) + 20n8 * (-3 + n) + n9(-3 + n)) = 0 (120960 + -40320n + -19008n + 6336n2 + -108840n2 + 36280n3 + -20940n3 + 6980n4 + 20250n4 + -6750n5 + 7911n5 + -2637n6 + (-3 * -30n6 + n * -30n6) + 120n7 * (-3 + n) + 20n8 * (-3 + n) + n9(-3 + n)) = 0 (120960 + -40320n + -19008n + 6336n2 + -108840n2 + 36280n3 + -20940n3 + 6980n4 + 20250n4 + -6750n5 + 7911n5 + -2637n6 + (90n6 + -30n7) + 120n7 * (-3 + n) + 20n8 * (-3 + n) + n9(-3 + n)) = 0 (120960 + -40320n + -19008n + 6336n2 + -108840n2 + 36280n3 + -20940n3 + 6980n4 + 20250n4 + -6750n5 + 7911n5 + -2637n6 + 90n6 + -30n7 + (-3 * 120n7 + n * 120n7) + 20n8 * (-3 + n) + n9(-3 + n)) = 0 (120960 + -40320n + -19008n + 6336n2 + -108840n2 + 36280n3 + -20940n3 + 6980n4 + 20250n4 + -6750n5 + 7911n5 + -2637n6 + 90n6 + -30n7 + (-360n7 + 120n8) + 20n8 * (-3 + n) + n9(-3 + n)) = 0 (120960 + -40320n + -19008n + 6336n2 + -108840n2 + 36280n3 + -20940n3 + 6980n4 + 20250n4 + -6750n5 + 7911n5 + -2637n6 + 90n6 + -30n7 + -360n7 + 120n8 + (-3 * 20n8 + n * 20n8) + n9(-3 + n)) = 0 (120960 + -40320n + -19008n + 6336n2 + -108840n2 + 36280n3 + -20940n3 + 6980n4 + 20250n4 + -6750n5 + 7911n5 + -2637n6 + 90n6 + -30n7 + -360n7 + 120n8 + (-60n8 + 20n9) + n9(-3 + n)) = 0 (120960 + -40320n + -19008n + 6336n2 + -108840n2 + 36280n3 + -20940n3 + 6980n4 + 20250n4 + -6750n5 + 7911n5 + -2637n6 + 90n6 + -30n7 + -360n7 + 120n8 + -60n8 + 20n9 + (-3 * n9 + n * n9)) = 0 (120960 + -40320n + -19008n + 6336n2 + -108840n2 + 36280n3 + -20940n3 + 6980n4 + 20250n4 + -6750n5 + 7911n5 + -2637n6 + 90n6 + -30n7 + -360n7 + 120n8 + -60n8 + 20n9 + (-3n9 + n10)) = 0 Combine like terms: -40320n + -19008n = -59328n (120960 + -59328n + 6336n2 + -108840n2 + 36280n3 + -20940n3 + 6980n4 + 20250n4 + -6750n5 + 7911n5 + -2637n6 + 90n6 + -30n7 + -360n7 + 120n8 + -60n8 + 20n9 + -3n9 + n10) = 0 Combine like terms: 6336n2 + -108840n2 = -102504n2 (120960 + -59328n + -102504n2 + 36280n3 + -20940n3 + 6980n4 + 20250n4 + -6750n5 + 7911n5 + -2637n6 + 90n6 + -30n7 + -360n7 + 120n8 + -60n8 + 20n9 + -3n9 + n10) = 0 Combine like terms: 36280n3 + -20940n3 = 15340n3 (120960 + -59328n + -102504n2 + 15340n3 + 6980n4 + 20250n4 + -6750n5 + 7911n5 + -2637n6 + 90n6 + -30n7 + -360n7 + 120n8 + -60n8 + 20n9 + -3n9 + n10) = 0 Combine like terms: 6980n4 + 20250n4 = 27230n4 (120960 + -59328n + -102504n2 + 15340n3 + 27230n4 + -6750n5 + 7911n5 + -2637n6 + 90n6 + -30n7 + -360n7 + 120n8 + -60n8 + 20n9 + -3n9 + n10) = 0 Combine like terms: -6750n5 + 7911n5 = 1161n5 (120960 + -59328n + -102504n2 + 15340n3 + 27230n4 + 1161n5 + -2637n6 + 90n6 + -30n7 + -360n7 + 120n8 + -60n8 + 20n9 + -3n9 + n10) = 0 Combine like terms: -2637n6 + 90n6 = -2547n6 (120960 + -59328n + -102504n2 + 15340n3 + 27230n4 + 1161n5 + -2547n6 + -30n7 + -360n7 + 120n8 + -60n8 + 20n9 + -3n9 + n10) = 0 Combine like terms: -30n7 + -360n7 = -390n7 (120960 + -59328n + -102504n2 + 15340n3 + 27230n4 + 1161n5 + -2547n6 + -390n7 + 120n8 + -60n8 + 20n9 + -3n9 + n10) = 0 Combine like terms: 120n8 + -60n8 = 60n8 (120960 + -59328n + -102504n2 + 15340n3 + 27230n4 + 1161n5 + -2547n6 + -390n7 + 60n8 + 20n9 + -3n9 + n10) = 0 Combine like terms: 20n9 + -3n9 = 17n9 (120960 + -59328n + -102504n2 + 15340n3 + 27230n4 + 1161n5 + -2547n6 + -390n7 + 60n8 + 17n9 + n10) = 0 Solving 120960 + -59328n + -102504n2 + 15340n3 + 27230n4 + 1161n5 + -2547n6 + -390n7 + 60n8 + 17n9 + n10 = 0 Solving for variable 'n'. The solution to this equation could not be determined.
| 4(2x+2)=-24 | | -5x-39=4(2x-5)-6 | | (8+n)(7+n)(6+n)(5+n)(4+n)(3+n)(2+n)(n-1)(n-2)(n-3)=0 | | 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 |