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Simplifying (6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(n + -1)(n + -2) = 0 Reorder the terms: (6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(n + -2) = 0 Reorder the terms: (6 + n)(5 + n)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n) = 0 Multiply (6 + n) * (5 + n) (6(5 + n) + n(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n) = 0 ((5 * 6 + n * 6) + n(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n) = 0 ((30 + 6n) + n(5 + n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n) = 0 (30 + 6n + (5 * n + n * n))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n) = 0 (30 + 6n + (5n + n2))(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n) = 0 Combine like terms: 6n + 5n = 11n (30 + 11n + n2)(4 + n)(3 + n)(2 + n)(-1 + n)(-2 + n) = 0 Multiply (30 + 11n + n2) * (4 + n) (30(4 + n) + 11n * (4 + n) + n2(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n) = 0 ((4 * 30 + n * 30) + 11n * (4 + n) + n2(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n) = 0 ((120 + 30n) + 11n * (4 + n) + n2(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n) = 0 (120 + 30n + (4 * 11n + n * 11n) + n2(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n) = 0 (120 + 30n + (44n + 11n2) + n2(4 + n))(3 + n)(2 + n)(-1 + n)(-2 + n) = 0 (120 + 30n + 44n + 11n2 + (4 * n2 + n * n2))(3 + n)(2 + n)(-1 + n)(-2 + n) = 0 (120 + 30n + 44n + 11n2 + (4n2 + n3))(3 + n)(2 + n)(-1 + n)(-2 + n) = 0 Combine like terms: 30n + 44n = 74n (120 + 74n + 11n2 + 4n2 + n3)(3 + n)(2 + n)(-1 + n)(-2 + n) = 0 Combine like terms: 11n2 + 4n2 = 15n2 (120 + 74n + 15n2 + n3)(3 + n)(2 + n)(-1 + n)(-2 + n) = 0 Multiply (120 + 74n + 15n2 + n3) * (3 + n) (120(3 + n) + 74n * (3 + n) + 15n2 * (3 + n) + n3(3 + n))(2 + n)(-1 + n)(-2 + n) = 0 ((3 * 120 + n * 120) + 74n * (3 + n) + 15n2 * (3 + n) + n3(3 + n))(2 + n)(-1 + n)(-2 + n) = 0 ((360 + 120n) + 74n * (3 + n) + 15n2 * (3 + n) + n3(3 + n))(2 + n)(-1 + n)(-2 + n) = 0 (360 + 120n + (3 * 74n + n * 74n) + 15n2 * (3 + n) + n3(3 + n))(2 + n)(-1 + n)(-2 + n) = 0 (360 + 120n + (222n + 74n2) + 15n2 * (3 + n) + n3(3 + n))(2 + n)(-1 + n)(-2 + n) = 0 (360 + 120n + 222n + 74n2 + (3 * 15n2 + n * 15n2) + n3(3 + n))(2 + n)(-1 + n)(-2 + n) = 0 (360 + 120n + 222n + 74n2 + (45n2 + 15n3) + n3(3 + n))(2 + n)(-1 + n)(-2 + n) = 0 (360 + 120n + 222n + 74n2 + 45n2 + 15n3 + (3 * n3 + n * n3))(2 + n)(-1 + n)(-2 + n) = 0 (360 + 120n + 222n + 74n2 + 45n2 + 15n3 + (3n3 + n4))(2 + n)(-1 + n)(-2 + n) = 0 Combine like terms: 120n + 222n = 342n (360 + 342n + 74n2 + 45n2 + 15n3 + 3n3 + n4)(2 + n)(-1 + n)(-2 + n) = 0 Combine like terms: 74n2 + 45n2 = 119n2 (360 + 342n + 119n2 + 15n3 + 3n3 + n4)(2 + n)(-1 + n)(-2 + n) = 0 Combine like terms: 15n3 + 3n3 = 18n3 (360 + 342n + 119n2 + 18n3 + n4)(2 + n)(-1 + n)(-2 + n) = 0 Multiply (360 + 342n + 119n2 + 18n3 + n4) * (2 + n) (360(2 + n) + 342n * (2 + n) + 119n2 * (2 + n) + 18n3 * (2 + n) + n4(2 + n))(-1 + n)(-2 + n) = 0 ((2 * 360 + n * 360) + 342n * (2 + n) + 119n2 * (2 + n) + 18n3 * (2 + n) + n4(2 + n))(-1 + n)(-2 + n) = 0 ((720 + 360n) + 342n * (2 + n) + 119n2 * (2 + n) + 18n3 * (2 + n) + n4(2 + n))(-1 + n)(-2 + n) = 0 (720 + 360n + (2 * 342n + n * 342n) + 119n2 * (2 + n) + 18n3 * (2 + n) + n4(2 + n))(-1 + n)(-2 + n) = 0 (720 + 360n + (684n + 342n2) + 119n2 * (2 + n) + 18n3 * (2 + n) + n4(2 + n))(-1 + n)(-2 + n) = 0 (720 + 360n + 684n + 342n2 + (2 * 119n2 + n * 119n2) + 18n3 * (2 + n) + n4(2 + n))(-1 + n)(-2 + n) = 0 (720 + 360n + 684n + 342n2 + (238n2 + 119n3) + 18n3 * (2 + n) + n4(2 + n))(-1 + n)(-2 + n) = 0 (720 + 360n + 684n + 342n2 + 238n2 + 119n3 + (2 * 18n3 + n * 18n3) + n4(2 + n))(-1 + n)(-2 + n) = 0 (720 + 360n + 684n + 342n2 + 238n2 + 119n3 + (36n3 + 18n4) + n4(2 + n))(-1 + n)(-2 + n) = 0 (720 + 360n + 684n + 342n2 + 238n2 + 119n3 + 36n3 + 18n4 + (2 * n4 + n * n4))(-1 + n)(-2 + n) = 0 (720 + 360n + 684n + 342n2 + 238n2 + 119n3 + 36n3 + 18n4 + (2n4 + n5))(-1 + n)(-2 + n) = 0 Combine like terms: 360n + 684n = 1044n (720 + 1044n + 342n2 + 238n2 + 119n3 + 36n3 + 18n4 + 2n4 + n5)(-1 + n)(-2 + n) = 0 Combine like terms: 342n2 + 238n2 = 580n2 (720 + 1044n + 580n2 + 119n3 + 36n3 + 18n4 + 2n4 + n5)(-1 + n)(-2 + n) = 0 Combine like terms: 119n3 + 36n3 = 155n3 (720 + 1044n + 580n2 + 155n3 + 18n4 + 2n4 + n5)(-1 + n)(-2 + n) = 0 Combine like terms: 18n4 + 2n4 = 20n4 (720 + 1044n + 580n2 + 155n3 + 20n4 + n5)(-1 + n)(-2 + n) = 0 Multiply (720 + 1044n + 580n2 + 155n3 + 20n4 + n5) * (-1 + n) (720(-1 + n) + 1044n * (-1 + n) + 580n2 * (-1 + n) + 155n3 * (-1 + n) + 20n4 * (-1 + n) + n5(-1 + n))(-2 + n) = 0 ((-1 * 720 + n * 720) + 1044n * (-1 + n) + 580n2 * (-1 + n) + 155n3 * (-1 + n) + 20n4 * (-1 + n) + n5(-1 + n))(-2 + n) = 0 ((-720 + 720n) + 1044n * (-1 + n) + 580n2 * (-1 + n) + 155n3 * (-1 + n) + 20n4 * (-1 + n) + n5(-1 + n))(-2 + n) = 0 (-720 + 720n + (-1 * 1044n + n * 1044n) + 580n2 * (-1 + n) + 155n3 * (-1 + n) + 20n4 * (-1 + n) + n5(-1 + n))(-2 + n) = 0 (-720 + 720n + (-1044n + 1044n2) + 580n2 * (-1 + n) + 155n3 * (-1 + n) + 20n4 * (-1 + n) + n5(-1 + n))(-2 + n) = 0 (-720 + 720n + -1044n + 1044n2 + (-1 * 580n2 + n * 580n2) + 155n3 * (-1 + n) + 20n4 * (-1 + n) + n5(-1 + n))(-2 + n) = 0 (-720 + 720n + -1044n + 1044n2 + (-580n2 + 580n3) + 155n3 * (-1 + n) + 20n4 * (-1 + n) + n5(-1 + n))(-2 + n) = 0 (-720 + 720n + -1044n + 1044n2 + -580n2 + 580n3 + (-1 * 155n3 + n * 155n3) + 20n4 * (-1 + n) + n5(-1 + n))(-2 + n) = 0 (-720 + 720n + -1044n + 1044n2 + -580n2 + 580n3 + (-155n3 + 155n4) + 20n4 * (-1 + n) + n5(-1 + n))(-2 + n) = 0 (-720 + 720n + -1044n + 1044n2 + -580n2 + 580n3 + -155n3 + 155n4 + (-1 * 20n4 + n * 20n4) + n5(-1 + n))(-2 + n) = 0 (-720 + 720n + -1044n + 1044n2 + -580n2 + 580n3 + -155n3 + 155n4 + (-20n4 + 20n5) + n5(-1 + n))(-2 + n) = 0 (-720 + 720n + -1044n + 1044n2 + -580n2 + 580n3 + -155n3 + 155n4 + -20n4 + 20n5 + (-1 * n5 + n * n5))(-2 + n) = 0 (-720 + 720n + -1044n + 1044n2 + -580n2 + 580n3 + -155n3 + 155n4 + -20n4 + 20n5 + (-1n5 + n6))(-2 + n) = 0 Combine like terms: 720n + -1044n = -324n (-720 + -324n + 1044n2 + -580n2 + 580n3 + -155n3 + 155n4 + -20n4 + 20n5 + -1n5 + n6)(-2 + n) = 0 Combine like terms: 1044n2 + -580n2 = 464n2 (-720 + -324n + 464n2 + 580n3 + -155n3 + 155n4 + -20n4 + 20n5 + -1n5 + n6)(-2 + n) = 0 Combine like terms: 580n3 + -155n3 = 425n3 (-720 + -324n + 464n2 + 425n3 + 155n4 + -20n4 + 20n5 + -1n5 + n6)(-2 + n) = 0 Combine like terms: 155n4 + -20n4 = 135n4 (-720 + -324n + 464n2 + 425n3 + 135n4 + 20n5 + -1n5 + n6)(-2 + n) = 0 Combine like terms: 20n5 + -1n5 = 19n5 (-720 + -324n + 464n2 + 425n3 + 135n4 + 19n5 + n6)(-2 + n) = 0 Multiply (-720 + -324n + 464n2 + 425n3 + 135n4 + 19n5 + n6) * (-2 + n) (-720(-2 + n) + -324n * (-2 + n) + 464n2 * (-2 + n) + 425n3 * (-2 + n) + 135n4 * (-2 + n) + 19n5 * (-2 + n) + n6(-2 + n)) = 0 ((-2 * -720 + n * -720) + -324n * (-2 + n) + 464n2 * (-2 + n) + 425n3 * (-2 + n) + 135n4 * (-2 + n) + 19n5 * (-2 + n) + n6(-2 + n)) = 0 ((1440 + -720n) + -324n * (-2 + n) + 464n2 * (-2 + n) + 425n3 * (-2 + n) + 135n4 * (-2 + n) + 19n5 * (-2 + n) + n6(-2 + n)) = 0 (1440 + -720n + (-2 * -324n + n * -324n) + 464n2 * (-2 + n) + 425n3 * (-2 + n) + 135n4 * (-2 + n) + 19n5 * (-2 + n) + n6(-2 + n)) = 0 (1440 + -720n + (648n + -324n2) + 464n2 * (-2 + n) + 425n3 * (-2 + n) + 135n4 * (-2 + n) + 19n5 * (-2 + n) + n6(-2 + n)) = 0 (1440 + -720n + 648n + -324n2 + (-2 * 464n2 + n * 464n2) + 425n3 * (-2 + n) + 135n4 * (-2 + n) + 19n5 * (-2 + n) + n6(-2 + n)) = 0 (1440 + -720n + 648n + -324n2 + (-928n2 + 464n3) + 425n3 * (-2 + n) + 135n4 * (-2 + n) + 19n5 * (-2 + n) + n6(-2 + n)) = 0 (1440 + -720n + 648n + -324n2 + -928n2 + 464n3 + (-2 * 425n3 + n * 425n3) + 135n4 * (-2 + n) + 19n5 * (-2 + n) + n6(-2 + n)) = 0 (1440 + -720n + 648n + -324n2 + -928n2 + 464n3 + (-850n3 + 425n4) + 135n4 * (-2 + n) + 19n5 * (-2 + n) + n6(-2 + n)) = 0 (1440 + -720n + 648n + -324n2 + -928n2 + 464n3 + -850n3 + 425n4 + (-2 * 135n4 + n * 135n4) + 19n5 * (-2 + n) + n6(-2 + n)) = 0 (1440 + -720n + 648n + -324n2 + -928n2 + 464n3 + -850n3 + 425n4 + (-270n4 + 135n5) + 19n5 * (-2 + n) + n6(-2 + n)) = 0 (1440 + -720n + 648n + -324n2 + -928n2 + 464n3 + -850n3 + 425n4 + -270n4 + 135n5 + (-2 * 19n5 + n * 19n5) + n6(-2 + n)) = 0 (1440 + -720n + 648n + -324n2 + -928n2 + 464n3 + -850n3 + 425n4 + -270n4 + 135n5 + (-38n5 + 19n6) + n6(-2 + n)) = 0 (1440 + -720n + 648n + -324n2 + -928n2 + 464n3 + -850n3 + 425n4 + -270n4 + 135n5 + -38n5 + 19n6 + (-2 * n6 + n * n6)) = 0 (1440 + -720n + 648n + -324n2 + -928n2 + 464n3 + -850n3 + 425n4 + -270n4 + 135n5 + -38n5 + 19n6 + (-2n6 + n7)) = 0 Combine like terms: -720n + 648n = -72n (1440 + -72n + -324n2 + -928n2 + 464n3 + -850n3 + 425n4 + -270n4 + 135n5 + -38n5 + 19n6 + -2n6 + n7) = 0 Combine like terms: -324n2 + -928n2 = -1252n2 (1440 + -72n + -1252n2 + 464n3 + -850n3 + 425n4 + -270n4 + 135n5 + -38n5 + 19n6 + -2n6 + n7) = 0 Combine like terms: 464n3 + -850n3 = -386n3 (1440 + -72n + -1252n2 + -386n3 + 425n4 + -270n4 + 135n5 + -38n5 + 19n6 + -2n6 + n7) = 0 Combine like terms: 425n4 + -270n4 = 155n4 (1440 + -72n + -1252n2 + -386n3 + 155n4 + 135n5 + -38n5 + 19n6 + -2n6 + n7) = 0 Combine like terms: 135n5 + -38n5 = 97n5 (1440 + -72n + -1252n2 + -386n3 + 155n4 + 97n5 + 19n6 + -2n6 + n7) = 0 Combine like terms: 19n6 + -2n6 = 17n6 (1440 + -72n + -1252n2 + -386n3 + 155n4 + 97n5 + 17n6 + n7) = 0 Solving 1440 + -72n + -1252n2 + -386n3 + 155n4 + 97n5 + 17n6 + n7 = 0 Solving for variable 'n'. The solution to this equation could not be determined.
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