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Simplifying (n + -4)(n + -5)(n + -6)(n + -7)(4 + n)(3 + n)(2 + n)(n + -1)(n + -2)(n + -3) = 0 Reorder the terms: (-4 + n)(n + -5)(n + -6)(n + -7)(4 + n)(3 + n)(2 + n)(n + -1)(n + -2)(n + -3) = 0 Reorder the terms: (-4 + n)(-5 + n)(n + -6)(n + -7)(4 + n)(3 + n)(2 + n)(n + -1)(n + -2)(n + -3) = 0 Reorder the terms: (-4 + n)(-5 + n)(-6 + n)(n + -7)(4 + n)(3 + n)(2 + n)(n + -1)(n + -2)(n + -3) = 0 Reorder the terms: (-4 + n)(-5 + n)(-6 + n)(-7 + n)(4 + n)(3 + n)(2 + n)(n + -1)(n + -2)(n + -3) = 0 Reorder the terms: (-4 + n)(-5 + n)(-6 + n)(-7 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(n + -2)(n + -3) = 0 Reorder the terms: (-4 + n)(-5 + n)(-6 + n)(-7 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(n + -3) = 0 Reorder the terms: (-4 + n)(-5 + n)(-6 + n)(-7 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Multiply (-4 + n) * (-5 + n) (-4(-5 + n) + n(-5 + n))(-6 + n)(-7 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((-5 * -4 + n * -4) + n(-5 + n))(-6 + n)(-7 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((20 + -4n) + n(-5 + n))(-6 + n)(-7 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (20 + -4n + (-5 * n + n * n))(-6 + n)(-7 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (20 + -4n + (-5n + n2))(-6 + n)(-7 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: -4n + -5n = -9n (20 + -9n + n2)(-6 + n)(-7 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Multiply (20 + -9n + n2) * (-6 + n) (20(-6 + n) + -9n * (-6 + n) + n2(-6 + n))(-7 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((-6 * 20 + n * 20) + -9n * (-6 + n) + n2(-6 + n))(-7 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((-120 + 20n) + -9n * (-6 + n) + n2(-6 + n))(-7 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-120 + 20n + (-6 * -9n + n * -9n) + n2(-6 + n))(-7 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-120 + 20n + (54n + -9n2) + n2(-6 + n))(-7 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-120 + 20n + 54n + -9n2 + (-6 * n2 + n * n2))(-7 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (-120 + 20n + 54n + -9n2 + (-6n2 + n3))(-7 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 20n + 54n = 74n (-120 + 74n + -9n2 + -6n2 + n3)(-7 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: -9n2 + -6n2 = -15n2 (-120 + 74n + -15n2 + n3)(-7 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Multiply (-120 + 74n + -15n2 + n3) * (-7 + n) (-120(-7 + n) + 74n * (-7 + n) + -15n2 * (-7 + n) + n3(-7 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((-7 * -120 + n * -120) + 74n * (-7 + n) + -15n2 * (-7 + n) + n3(-7 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((840 + -120n) + 74n * (-7 + n) + -15n2 * (-7 + n) + n3(-7 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (840 + -120n + (-7 * 74n + n * 74n) + -15n2 * (-7 + n) + n3(-7 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (840 + -120n + (-518n + 74n2) + -15n2 * (-7 + n) + n3(-7 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (840 + -120n + -518n + 74n2 + (-7 * -15n2 + n * -15n2) + n3(-7 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (840 + -120n + -518n + 74n2 + (105n2 + -15n3) + n3(-7 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (840 + -120n + -518n + 74n2 + 105n2 + -15n3 + (-7 * n3 + n * n3))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (840 + -120n + -518n + 74n2 + 105n2 + -15n3 + (-7n3 + n4))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: -120n + -518n = -638n (840 + -638n + 74n2 + 105n2 + -15n3 + -7n3 + n4)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 74n2 + 105n2 = 179n2 (840 + -638n + 179n2 + -15n3 + -7n3 + n4)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: -15n3 + -7n3 = -22n3 (840 + -638n + 179n2 + -22n3 + n4)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Multiply (840 + -638n + 179n2 + -22n3 + n4) * (4 + n) (840(4 + n) + -638n * (4 + n) + 179n2 * (4 + n) + -22n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((4 * 840 + n * 840) + -638n * (4 + n) + 179n2 * (4 + n) + -22n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 ((3360 + 840n) + -638n * (4 + n) + 179n2 * (4 + n) + -22n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (3360 + 840n + (4 * -638n + n * -638n) + 179n2 * (4 + n) + -22n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (3360 + 840n + (-2552n + -638n2) + 179n2 * (4 + n) + -22n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (3360 + 840n + -2552n + -638n2 + (4 * 179n2 + n * 179n2) + -22n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (3360 + 840n + -2552n + -638n2 + (716n2 + 179n3) + -22n3 * (4 + n) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (3360 + 840n + -2552n + -638n2 + 716n2 + 179n3 + (4 * -22n3 + n * -22n3) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (3360 + 840n + -2552n + -638n2 + 716n2 + 179n3 + (-88n3 + -22n4) + n4(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (3360 + 840n + -2552n + -638n2 + 716n2 + 179n3 + -88n3 + -22n4 + (4 * n4 + n * n4))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 (3360 + 840n + -2552n + -638n2 + 716n2 + 179n3 + -88n3 + -22n4 + (4n4 + n5))(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 840n + -2552n = -1712n (3360 + -1712n + -638n2 + 716n2 + 179n3 + -88n3 + -22n4 + 4n4 + n5)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: -638n2 + 716n2 = 78n2 (3360 + -1712n + 78n2 + 179n3 + -88n3 + -22n4 + 4n4 + n5)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 179n3 + -88n3 = 91n3 (3360 + -1712n + 78n2 + 91n3 + -22n4 + 4n4 + n5)(3 + n)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: -22n4 + 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 = -1776n (10080 + -1776n + -1712n2 + 234n2 + 78n3 + 273n3 + 91n4 + -54n4 + -18n5 + 3n5 + n6)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: -1712n2 + 234n2 = -1478n2 (10080 + -1776n + -1478n2 + 78n3 + 273n3 + 91n4 + -54n4 + -18n5 + 3n5 + n6)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 78n3 + 273n3 = 351n3 (10080 + -1776n + -1478n2 + 351n3 + 91n4 + -54n4 + -18n5 + 3n5 + n6)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 91n4 + -54n4 = 37n4 (10080 + -1776n + -1478n2 + 351n3 + 37n4 + -18n5 + 3n5 + n6)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: -18n5 + 3n5 = -15n5 (10080 + -1776n + -1478n2 + 351n3 + 37n4 + -15n5 + n6)(2 + n)(-1 + n)(-2 + n)(-3 + n) = 0 Multiply (10080 + -1776n + -1478n2 + 351n3 + 37n4 + -15n5 + n6) * (2 + n) (10080(2 + n) + -1776n * (2 + n) + -1478n2 * (2 + n) + 351n3 * (2 + n) + 37n4 * (2 + n) + -15n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 ((2 * 10080 + n * 10080) + -1776n * (2 + n) + -1478n2 * (2 + n) + 351n3 * (2 + n) + 37n4 * (2 + n) + -15n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 ((20160 + 10080n) + -1776n * (2 + n) + -1478n2 * (2 + n) + 351n3 * (2 + n) + 37n4 * (2 + n) + -15n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (20160 + 10080n + (2 * -1776n + n * -1776n) + -1478n2 * (2 + n) + 351n3 * (2 + n) + 37n4 * (2 + n) + -15n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (20160 + 10080n + (-3552n + -1776n2) + -1478n2 * (2 + n) + 351n3 * (2 + n) + 37n4 * (2 + n) + -15n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (20160 + 10080n + -3552n + -1776n2 + (2 * -1478n2 + n * -1478n2) + 351n3 * (2 + n) + 37n4 * (2 + n) + -15n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (20160 + 10080n + -3552n + -1776n2 + (-2956n2 + -1478n3) + 351n3 * (2 + n) + 37n4 * (2 + n) + -15n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (20160 + 10080n + -3552n + -1776n2 + -2956n2 + -1478n3 + (2 * 351n3 + n * 351n3) + 37n4 * (2 + n) + -15n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (20160 + 10080n + -3552n + -1776n2 + -2956n2 + -1478n3 + (702n3 + 351n4) + 37n4 * (2 + n) + -15n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (20160 + 10080n + -3552n + -1776n2 + -2956n2 + -1478n3 + 702n3 + 351n4 + (2 * 37n4 + n * 37n4) + -15n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (20160 + 10080n + -3552n + -1776n2 + -2956n2 + -1478n3 + 702n3 + 351n4 + (74n4 + 37n5) + -15n5 * (2 + n) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (20160 + 10080n + -3552n + -1776n2 + -2956n2 + -1478n3 + 702n3 + 351n4 + 74n4 + 37n5 + (2 * -15n5 + n * -15n5) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (20160 + 10080n + -3552n + -1776n2 + -2956n2 + -1478n3 + 702n3 + 351n4 + 74n4 + 37n5 + (-30n5 + -15n6) + n6(2 + n))(-1 + n)(-2 + n)(-3 + n) = 0 (20160 + 10080n + -3552n + -1776n2 + -2956n2 + -1478n3 + 702n3 + 351n4 + 74n4 + 37n5 + -30n5 + -15n6 + (2 * n6 + n * n6))(-1 + n)(-2 + n)(-3 + n) = 0 (20160 + 10080n + -3552n + -1776n2 + -2956n2 + -1478n3 + 702n3 + 351n4 + 74n4 + 37n5 + -30n5 + -15n6 + (2n6 + n7))(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 10080n + -3552n = 6528n (20160 + 6528n + -1776n2 + -2956n2 + -1478n3 + 702n3 + 351n4 + 74n4 + 37n5 + -30n5 + -15n6 + 2n6 + n7)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: -1776n2 + -2956n2 = -4732n2 (20160 + 6528n + -4732n2 + -1478n3 + 702n3 + 351n4 + 74n4 + 37n5 + -30n5 + -15n6 + 2n6 + n7)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: -1478n3 + 702n3 = -776n3 (20160 + 6528n + -4732n2 + -776n3 + 351n4 + 74n4 + 37n5 + -30n5 + -15n6 + 2n6 + n7)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 351n4 + 74n4 = 425n4 (20160 + 6528n + -4732n2 + -776n3 + 425n4 + 37n5 + -30n5 + -15n6 + 2n6 + n7)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: 37n5 + -30n5 = 7n5 (20160 + 6528n + -4732n2 + -776n3 + 425n4 + 7n5 + -15n6 + 2n6 + n7)(-1 + n)(-2 + n)(-3 + n) = 0 Combine like terms: -15n6 + 2n6 = -13n6 (20160 + 6528n + -4732n2 + -776n3 + 425n4 + 7n5 + -13n6 + n7)(-1 + n)(-2 + n)(-3 + n) = 0 Multiply (20160 + 6528n + -4732n2 + -776n3 + 425n4 + 7n5 + -13n6 + n7) * (-1 + n) (20160(-1 + n) + 6528n * (-1 + n) + -4732n2 * (-1 + n) + -776n3 * (-1 + n) + 425n4 * (-1 + n) + 7n5 * (-1 + n) + -13n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 ((-1 * 20160 + n * 20160) + 6528n * (-1 + n) + -4732n2 * (-1 + n) + -776n3 * (-1 + n) + 425n4 * (-1 + n) + 7n5 * (-1 + n) + -13n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 ((-20160 + 20160n) + 6528n * (-1 + n) + -4732n2 * (-1 + n) + -776n3 * (-1 + n) + 425n4 * (-1 + n) + 7n5 * (-1 + n) + -13n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-20160 + 20160n + (-1 * 6528n + n * 6528n) + -4732n2 * (-1 + n) + -776n3 * (-1 + n) + 425n4 * (-1 + n) + 7n5 * (-1 + n) + -13n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-20160 + 20160n + (-6528n + 6528n2) + -4732n2 * (-1 + n) + -776n3 * (-1 + n) + 425n4 * (-1 + n) + 7n5 * (-1 + n) + -13n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-20160 + 20160n + -6528n + 6528n2 + (-1 * -4732n2 + n * -4732n2) + -776n3 * (-1 + n) + 425n4 * (-1 + n) + 7n5 * (-1 + n) + -13n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-20160 + 20160n + -6528n + 6528n2 + (4732n2 + -4732n3) + -776n3 * (-1 + n) + 425n4 * (-1 + n) + 7n5 * (-1 + n) + -13n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-20160 + 20160n + -6528n + 6528n2 + 4732n2 + -4732n3 + (-1 * -776n3 + n * -776n3) + 425n4 * (-1 + n) + 7n5 * (-1 + n) + -13n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-20160 + 20160n + -6528n + 6528n2 + 4732n2 + -4732n3 + (776n3 + -776n4) + 425n4 * (-1 + n) + 7n5 * (-1 + n) + -13n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-20160 + 20160n + -6528n + 6528n2 + 4732n2 + -4732n3 + 776n3 + -776n4 + (-1 * 425n4 + n * 425n4) + 7n5 * (-1 + n) + -13n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-20160 + 20160n + -6528n + 6528n2 + 4732n2 + -4732n3 + 776n3 + -776n4 + (-425n4 + 425n5) + 7n5 * (-1 + n) + -13n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-20160 + 20160n + -6528n + 6528n2 + 4732n2 + -4732n3 + 776n3 + -776n4 + -425n4 + 425n5 + (-1 * 7n5 + n * 7n5) + -13n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-20160 + 20160n + -6528n + 6528n2 + 4732n2 + -4732n3 + 776n3 + -776n4 + -425n4 + 425n5 + (-7n5 + 7n6) + -13n6 * (-1 + n) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-20160 + 20160n + -6528n + 6528n2 + 4732n2 + -4732n3 + 776n3 + -776n4 + -425n4 + 425n5 + -7n5 + 7n6 + (-1 * -13n6 + n * -13n6) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-20160 + 20160n + -6528n + 6528n2 + 4732n2 + -4732n3 + 776n3 + -776n4 + -425n4 + 425n5 + -7n5 + 7n6 + (13n6 + -13n7) + n7(-1 + n))(-2 + n)(-3 + n) = 0 (-20160 + 20160n + -6528n + 6528n2 + 4732n2 + -4732n3 + 776n3 + -776n4 + -425n4 + 425n5 + -7n5 + 7n6 + 13n6 + -13n7 + (-1 * n7 + n * n7))(-2 + n)(-3 + n) = 0 (-20160 + 20160n + -6528n + 6528n2 + 4732n2 + -4732n3 + 776n3 + -776n4 + -425n4 + 425n5 + -7n5 + 7n6 + 13n6 + -13n7 + (-1n7 + n8))(-2 + n)(-3 + n) = 0 Combine like terms: 20160n + -6528n = 13632n (-20160 + 13632n + 6528n2 + 4732n2 + -4732n3 + 776n3 + -776n4 + -425n4 + 425n5 + -7n5 + 7n6 + 13n6 + -13n7 + -1n7 + n8)(-2 + n)(-3 + n) = 0 Combine like terms: 6528n2 + 4732n2 = 11260n2 (-20160 + 13632n + 11260n2 + -4732n3 + 776n3 + -776n4 + -425n4 + 425n5 + -7n5 + 7n6 + 13n6 + -13n7 + -1n7 + n8)(-2 + n)(-3 + n) = 0 Combine like terms: -4732n3 + 776n3 = -3956n3 (-20160 + 13632n + 11260n2 + -3956n3 + -776n4 + -425n4 + 425n5 + -7n5 + 7n6 + 13n6 + -13n7 + -1n7 + n8)(-2 + n)(-3 + n) = 0 Combine like terms: -776n4 + -425n4 = -1201n4 (-20160 + 13632n + 11260n2 + -3956n3 + -1201n4 + 425n5 + -7n5 + 7n6 + 13n6 + -13n7 + -1n7 + n8)(-2 + n)(-3 + n) = 0 Combine like terms: 425n5 + -7n5 = 418n5 (-20160 + 13632n + 11260n2 + -3956n3 + -1201n4 + 418n5 + 7n6 + 13n6 + -13n7 + -1n7 + n8)(-2 + n)(-3 + n) = 0 Combine like terms: 7n6 + 13n6 = 20n6 (-20160 + 13632n + 11260n2 + -3956n3 + -1201n4 + 418n5 + 20n6 + -13n7 + -1n7 + n8)(-2 + n)(-3 + n) = 0 Combine like terms: -13n7 + -1n7 = -14n7 (-20160 + 13632n + 11260n2 + -3956n3 + -1201n4 + 418n5 + 20n6 + -14n7 + n8)(-2 + n)(-3 + n) = 0 Multiply (-20160 + 13632n + 11260n2 + -3956n3 + -1201n4 + 418n5 + 20n6 + -14n7 + n8) * (-2 + n) (-20160(-2 + n) + 13632n * (-2 + n) + 11260n2 * (-2 + n) + -3956n3 * (-2 + n) + -1201n4 * (-2 + n) + 418n5 * (-2 + n) + 20n6 * (-2 + n) + -14n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 ((-2 * -20160 + n * -20160) + 13632n * (-2 + n) + 11260n2 * (-2 + n) + -3956n3 * (-2 + n) + -1201n4 * (-2 + n) + 418n5 * (-2 + n) + 20n6 * (-2 + n) + -14n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 ((40320 + -20160n) + 13632n * (-2 + n) + 11260n2 * (-2 + n) + -3956n3 * (-2 + n) + -1201n4 * (-2 + n) + 418n5 * (-2 + n) + 20n6 * (-2 + n) + -14n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (40320 + -20160n + (-2 * 13632n + n * 13632n) + 11260n2 * (-2 + n) + -3956n3 * (-2 + n) + -1201n4 * (-2 + n) + 418n5 * (-2 + n) + 20n6 * (-2 + n) + -14n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (40320 + -20160n + (-27264n + 13632n2) + 11260n2 * (-2 + n) + -3956n3 * (-2 + n) + -1201n4 * (-2 + n) + 418n5 * (-2 + n) + 20n6 * (-2 + n) + -14n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (40320 + -20160n + -27264n + 13632n2 + (-2 * 11260n2 + n * 11260n2) + -3956n3 * (-2 + n) + -1201n4 * (-2 + n) + 418n5 * (-2 + n) + 20n6 * (-2 + n) + -14n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (40320 + -20160n + -27264n + 13632n2 + (-22520n2 + 11260n3) + -3956n3 * (-2 + n) + -1201n4 * (-2 + n) + 418n5 * (-2 + n) + 20n6 * (-2 + n) + -14n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (40320 + -20160n + -27264n + 13632n2 + -22520n2 + 11260n3 + (-2 * -3956n3 + n * -3956n3) + -1201n4 * (-2 + n) + 418n5 * (-2 + n) + 20n6 * (-2 + n) + -14n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (40320 + -20160n + -27264n + 13632n2 + -22520n2 + 11260n3 + (7912n3 + -3956n4) + -1201n4 * (-2 + n) + 418n5 * (-2 + n) + 20n6 * (-2 + n) + -14n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (40320 + -20160n + -27264n + 13632n2 + -22520n2 + 11260n3 + 7912n3 + -3956n4 + (-2 * -1201n4 + n * -1201n4) + 418n5 * (-2 + n) + 20n6 * (-2 + n) + -14n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (40320 + -20160n + -27264n + 13632n2 + -22520n2 + 11260n3 + 7912n3 + -3956n4 + (2402n4 + -1201n5) + 418n5 * (-2 + n) + 20n6 * (-2 + n) + -14n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (40320 + -20160n + -27264n + 13632n2 + -22520n2 + 11260n3 + 7912n3 + -3956n4 + 2402n4 + -1201n5 + (-2 * 418n5 + n * 418n5) + 20n6 * (-2 + n) + -14n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (40320 + -20160n + -27264n + 13632n2 + -22520n2 + 11260n3 + 7912n3 + -3956n4 + 2402n4 + -1201n5 + (-836n5 + 418n6) + 20n6 * (-2 + n) + -14n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (40320 + -20160n + -27264n + 13632n2 + -22520n2 + 11260n3 + 7912n3 + -3956n4 + 2402n4 + -1201n5 + -836n5 + 418n6 + (-2 * 20n6 + n * 20n6) + -14n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (40320 + -20160n + -27264n + 13632n2 + -22520n2 + 11260n3 + 7912n3 + -3956n4 + 2402n4 + -1201n5 + -836n5 + 418n6 + (-40n6 + 20n7) + -14n7 * (-2 + n) + n8(-2 + n))(-3 + n) = 0 (40320 + -20160n + -27264n + 13632n2 + -22520n2 + 11260n3 + 7912n3 + -3956n4 + 2402n4 + -1201n5 + -836n5 + 418n6 + -40n6 + 20n7 + (-2 * -14n7 + n * -14n7) + n8(-2 + n))(-3 + n) = 0 (40320 + -20160n + -27264n + 13632n2 + -22520n2 + 11260n3 + 7912n3 + -3956n4 + 2402n4 + -1201n5 + -836n5 + 418n6 + -40n6 + 20n7 + (28n7 + -14n8) + n8(-2 + n))(-3 + n) = 0 (40320 + -20160n + -27264n + 13632n2 + -22520n2 + 11260n3 + 7912n3 + -3956n4 + 2402n4 + -1201n5 + -836n5 + 418n6 + -40n6 + 20n7 + 28n7 + -14n8 + (-2 * n8 + n * n8))(-3 + n) = 0 (40320 + -20160n + -27264n + 13632n2 + -22520n2 + 11260n3 + 7912n3 + -3956n4 + 2402n4 + -1201n5 + -836n5 + 418n6 + -40n6 + 20n7 + 28n7 + -14n8 + (-2n8 + n9))(-3 + n) = 0 Combine like terms: -20160n + -27264n = -47424n (40320 + -47424n + 13632n2 + -22520n2 + 11260n3 + 7912n3 + -3956n4 + 2402n4 + -1201n5 + -836n5 + 418n6 + -40n6 + 20n7 + 28n7 + -14n8 + -2n8 + n9)(-3 + n) = 0 Combine like terms: 13632n2 + -22520n2 = -8888n2 (40320 + -47424n + -8888n2 + 11260n3 + 7912n3 + -3956n4 + 2402n4 + -1201n5 + -836n5 + 418n6 + -40n6 + 20n7 + 28n7 + -14n8 + -2n8 + n9)(-3 + n) = 0 Combine like terms: 11260n3 + 7912n3 = 19172n3 (40320 + -47424n + -8888n2 + 19172n3 + -3956n4 + 2402n4 + -1201n5 + -836n5 + 418n6 + -40n6 + 20n7 + 28n7 + -14n8 + -2n8 + n9)(-3 + n) = 0 Combine like terms: -3956n4 + 2402n4 = -1554n4 (40320 + -47424n + -8888n2 + 19172n3 + -1554n4 + -1201n5 + -836n5 + 418n6 + -40n6 + 20n7 + 28n7 + -14n8 + -2n8 + n9)(-3 + n) = 0 Combine like terms: -1201n5 + -836n5 = -2037n5 (40320 + -47424n + -8888n2 + 19172n3 + -1554n4 + -2037n5 + 418n6 + -40n6 + 20n7 + 28n7 + -14n8 + -2n8 + n9)(-3 + n) = 0 Combine like terms: 418n6 + -40n6 = 378n6 (40320 + -47424n + -8888n2 + 19172n3 + -1554n4 + -2037n5 + 378n6 + 20n7 + 28n7 + -14n8 + -2n8 + n9)(-3 + n) = 0 Combine like terms: 20n7 + 28n7 = 48n7 (40320 + -47424n + -8888n2 + 19172n3 + -1554n4 + -2037n5 + 378n6 + 48n7 + -14n8 + -2n8 + n9)(-3 + n) = 0 Combine like terms: -14n8 + -2n8 = -16n8 (40320 + -47424n + -8888n2 + 19172n3 + -1554n4 + -2037n5 + 378n6 + 48n7 + -16n8 + n9)(-3 + n) = 0 Multiply (40320 + -47424n + -8888n2 + 19172n3 + -1554n4 + -2037n5 + 378n6 + 48n7 + -16n8 + n9) * (-3 + n) (40320(-3 + n) + -47424n * (-3 + n) + -8888n2 * (-3 + n) + 19172n3 * (-3 + n) + -1554n4 * (-3 + n) + -2037n5 * (-3 + n) + 378n6 * (-3 + n) + 48n7 * (-3 + n) + -16n8 * (-3 + n) + n9(-3 + n)) = 0 ((-3 * 40320 + n * 40320) + -47424n * (-3 + n) + -8888n2 * (-3 + n) + 19172n3 * (-3 + n) + -1554n4 * (-3 + n) + -2037n5 * (-3 + n) + 378n6 * (-3 + n) + 48n7 * (-3 + n) + -16n8 * (-3 + n) + n9(-3 + n)) = 0 ((-120960 + 40320n) + -47424n * (-3 + n) + -8888n2 * (-3 + n) + 19172n3 * (-3 + n) + -1554n4 * (-3 + n) + -2037n5 * (-3 + n) + 378n6 * (-3 + n) + 48n7 * (-3 + n) + -16n8 * (-3 + n) + n9(-3 + n)) = 0 (-120960 + 40320n + (-3 * -47424n + n * -47424n) + -8888n2 * (-3 + n) + 19172n3 * (-3 + n) + -1554n4 * (-3 + n) + -2037n5 * (-3 + n) + 378n6 * (-3 + n) + 48n7 * (-3 + n) + -16n8 * (-3 + n) + n9(-3 + n)) = 0 (-120960 + 40320n + (142272n + -47424n2) + -8888n2 * (-3 + n) + 19172n3 * (-3 + n) + -1554n4 * (-3 + n) + -2037n5 * (-3 + n) + 378n6 * (-3 + n) + 48n7 * (-3 + n) + -16n8 * (-3 + n) + n9(-3 + n)) = 0 (-120960 + 40320n + 142272n + -47424n2 + (-3 * -8888n2 + n * -8888n2) + 19172n3 * (-3 + n) + -1554n4 * (-3 + n) + -2037n5 * (-3 + n) + 378n6 * (-3 + n) + 48n7 * (-3 + n) + -16n8 * (-3 + n) + n9(-3 + n)) = 0 (-120960 + 40320n + 142272n + -47424n2 + (26664n2 + -8888n3) + 19172n3 * (-3 + n) + -1554n4 * (-3 + n) + -2037n5 * (-3 + n) + 378n6 * (-3 + n) + 48n7 * (-3 + n) + -16n8 * (-3 + n) + n9(-3 + n)) = 0 (-120960 + 40320n + 142272n + -47424n2 + 26664n2 + -8888n3 + (-3 * 19172n3 + n * 19172n3) + -1554n4 * (-3 + n) + -2037n5 * (-3 + n) + 378n6 * (-3 + n) + 48n7 * (-3 + n) + -16n8 * (-3 + n) + n9(-3 + n)) = 0 (-120960 + 40320n + 142272n + -47424n2 + 26664n2 + -8888n3 + (-57516n3 + 19172n4) + -1554n4 * (-3 + n) + -2037n5 * (-3 + n) + 378n6 * (-3 + n) + 48n7 * (-3 + n) + -16n8 * (-3 + n) + n9(-3 + n)) = 0 (-120960 + 40320n + 142272n + -47424n2 + 26664n2 + -8888n3 + -57516n3 + 19172n4 + (-3 * -1554n4 + n * -1554n4) + -2037n5 * (-3 + n) + 378n6 * (-3 + n) + 48n7 * (-3 + n) + -16n8 * (-3 + n) + n9(-3 + n)) = 0 (-120960 + 40320n + 142272n + -47424n2 + 26664n2 + -8888n3 + -57516n3 + 19172n4 + (4662n4 + -1554n5) + -2037n5 * (-3 + n) + 378n6 * (-3 + n) + 48n7 * (-3 + n) + -16n8 * (-3 + n) + n9(-3 + n)) = 0 (-120960 + 40320n + 142272n + -47424n2 + 26664n2 + -8888n3 + -57516n3 + 19172n4 + 4662n4 + -1554n5 + (-3 * -2037n5 + n * -2037n5) + 378n6 * (-3 + n) + 48n7 * (-3 + n) + -16n8 * (-3 + n) + n9(-3 + n)) = 0 (-120960 + 40320n + 142272n + -47424n2 + 26664n2 + -8888n3 + -57516n3 + 19172n4 + 4662n4 + -1554n5 + (6111n5 + -2037n6) + 378n6 * (-3 + n) + 48n7 * (-3 + n) + -16n8 * (-3 + n) + n9(-3 + n)) = 0 (-120960 + 40320n + 142272n + -47424n2 + 26664n2 + -8888n3 + -57516n3 + 19172n4 + 4662n4 + -1554n5 + 6111n5 + -2037n6 + (-3 * 378n6 + n * 378n6) + 48n7 * (-3 + n) + -16n8 * (-3 + n) + n9(-3 + n)) = 0 (-120960 + 40320n + 142272n + -47424n2 + 26664n2 + -8888n3 + -57516n3 + 19172n4 + 4662n4 + -1554n5 + 6111n5 + -2037n6 + (-1134n6 + 378n7) + 48n7 * (-3 + n) + -16n8 * (-3 + n) + n9(-3 + n)) = 0 (-120960 + 40320n + 142272n + -47424n2 + 26664n2 + -8888n3 + -57516n3 + 19172n4 + 4662n4 + -1554n5 + 6111n5 + -2037n6 + -1134n6 + 378n7 + (-3 * 48n7 + n * 48n7) + -16n8 * (-3 + n) + n9(-3 + n)) = 0 (-120960 + 40320n + 142272n + -47424n2 + 26664n2 + -8888n3 + -57516n3 + 19172n4 + 4662n4 + -1554n5 + 6111n5 + -2037n6 + -1134n6 + 378n7 + (-144n7 + 48n8) + -16n8 * (-3 + n) + n9(-3 + n)) = 0 (-120960 + 40320n + 142272n + -47424n2 + 26664n2 + -8888n3 + -57516n3 + 19172n4 + 4662n4 + -1554n5 + 6111n5 + -2037n6 + -1134n6 + 378n7 + -144n7 + 48n8 + (-3 * -16n8 + n * -16n8) + n9(-3 + n)) = 0 (-120960 + 40320n + 142272n + -47424n2 + 26664n2 + -8888n3 + -57516n3 + 19172n4 + 4662n4 + -1554n5 + 6111n5 + -2037n6 + -1134n6 + 378n7 + -144n7 + 48n8 + (48n8 + -16n9) + n9(-3 + n)) = 0 (-120960 + 40320n + 142272n + -47424n2 + 26664n2 + -8888n3 + -57516n3 + 19172n4 + 4662n4 + -1554n5 + 6111n5 + -2037n6 + -1134n6 + 378n7 + -144n7 + 48n8 + 48n8 + -16n9 + (-3 * n9 + n * n9)) = 0 (-120960 + 40320n + 142272n + -47424n2 + 26664n2 + -8888n3 + -57516n3 + 19172n4 + 4662n4 + -1554n5 + 6111n5 + -2037n6 + -1134n6 + 378n7 + -144n7 + 48n8 + 48n8 + -16n9 + (-3n9 + n10)) = 0 Combine like terms: 40320n + 142272n = 182592n (-120960 + 182592n + -47424n2 + 26664n2 + -8888n3 + -57516n3 + 19172n4 + 4662n4 + -1554n5 + 6111n5 + -2037n6 + -1134n6 + 378n7 + -144n7 + 48n8 + 48n8 + -16n9 + -3n9 + n10) = 0 Combine like terms: -47424n2 + 26664n2 = -20760n2 (-120960 + 182592n + -20760n2 + -8888n3 + -57516n3 + 19172n4 + 4662n4 + -1554n5 + 6111n5 + -2037n6 + -1134n6 + 378n7 + -144n7 + 48n8 + 48n8 + -16n9 + -3n9 + n10) = 0 Combine like terms: -8888n3 + -57516n3 = -66404n3 (-120960 + 182592n + -20760n2 + -66404n3 + 19172n4 + 4662n4 + -1554n5 + 6111n5 + -2037n6 + -1134n6 + 378n7 + -144n7 + 48n8 + 48n8 + -16n9 + -3n9 + n10) = 0 Combine like terms: 19172n4 + 4662n4 = 23834n4 (-120960 + 182592n + -20760n2 + -66404n3 + 23834n4 + -1554n5 + 6111n5 + -2037n6 + -1134n6 + 378n7 + -144n7 + 48n8 + 48n8 + -16n9 + -3n9 + n10) = 0 Combine like terms: -1554n5 + 6111n5 = 4557n5 (-120960 + 182592n + -20760n2 + -66404n3 + 23834n4 + 4557n5 + -2037n6 + -1134n6 + 378n7 + -144n7 + 48n8 + 48n8 + -16n9 + -3n9 + n10) = 0 Combine like terms: -2037n6 + -1134n6 = -3171n6 (-120960 + 182592n + -20760n2 + -66404n3 + 23834n4 + 4557n5 + -3171n6 + 378n7 + -144n7 + 48n8 + 48n8 + -16n9 + -3n9 + n10) = 0 Combine like terms: 378n7 + -144n7 = 234n7 (-120960 + 182592n + -20760n2 + -66404n3 + 23834n4 + 4557n5 + -3171n6 + 234n7 + 48n8 + 48n8 + -16n9 + -3n9 + n10) = 0 Combine like terms: 48n8 + 48n8 = 96n8 (-120960 + 182592n + -20760n2 + -66404n3 + 23834n4 + 4557n5 + -3171n6 + 234n7 + 96n8 + -16n9 + -3n9 + n10) = 0 Combine like terms: -16n9 + -3n9 = -19n9 (-120960 + 182592n + -20760n2 + -66404n3 + 23834n4 + 4557n5 + -3171n6 + 234n7 + 96n8 + -19n9 + n10) = 0 Solving -120960 + 182592n + -20760n2 + -66404n3 + 23834n4 + 4557n5 + -3171n6 + 234n7 + 96n8 + -19n9 + n10 = 0 Solving for variable 'n'. The solution to this equation could not be determined.
| y^2=-8x+12 | | 2x^2-4x-10= | | 39=7x+2x^2 | | 8x-4=3(x+4)+5x | | 3y^2+24x-12=0 | | 3(8y)+y=-1 | | 7-(x+4)=O | | (n-4)(n-5)(n-6)(5+n)(4+n)(3+n)(2+n)(n-1)(n-2)(n-3)=0 | | 6x-20.00=20 | | x^2-5.5x-42=0 | | (q-9)*3=15 | | (e+1)*5=30 | | (e+3)*2=8 | | ln(x)*ln(x)=e | | ln(x)= | | 9.5-.075x=20 | | 5x+=3x+7 | | -51+13x=14x-22 | | -2x+18=6(1-2x)+4x | | 6x+11x=35 | | 4m+7=36 | | 5x-1=26+4x | | (20n-7.8).2=14.2 | | 8m+8=88 | | 3x-5y+8z=60 | | (31.2-7n)-.3=0.456 | | log(4)(5x+1)-log(4)x=1+log(4)3 | | (n-4)(n-5)(6+n)(5+n)(4+n)(3+n)(2+n)(n-1)(n-2)(n-3)=0 | | 9x-9=26 | | 2x+4x+1=3x+7 | | 14(-9-4m)=21 | | 498-3x^8=216 |