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Simplifying n(n + 1)(n + 2)(n + 3)(n + 4) = 0 Reorder the terms: n(1 + n)(n + 2)(n + 3)(n + 4) = 0 Reorder the terms: n(1 + n)(2 + n)(n + 3)(n + 4) = 0 Reorder the terms: n(1 + n)(2 + n)(3 + n)(n + 4) = 0 Reorder the terms: n(1 + n)(2 + n)(3 + n)(4 + n) = 0 Multiply (1 + n) * (2 + n) n(1(2 + n) + n(2 + n))(3 + n)(4 + n) = 0 n((2 * 1 + n * 1) + n(2 + n))(3 + n)(4 + n) = 0 n((2 + 1n) + n(2 + n))(3 + n)(4 + n) = 0 n(2 + 1n + (2 * n + n * n))(3 + n)(4 + n) = 0 n(2 + 1n + (2n + n2))(3 + n)(4 + n) = 0 Combine like terms: 1n + 2n = 3n n(2 + 3n + n2)(3 + n)(4 + n) = 0 Multiply (2 + 3n + n2) * (3 + n) n(2(3 + n) + 3n * (3 + n) + n2(3 + n))(4 + n) = 0 n((3 * 2 + n * 2) + 3n * (3 + n) + n2(3 + n))(4 + n) = 0 n((6 + 2n) + 3n * (3 + n) + n2(3 + n))(4 + n) = 0 n(6 + 2n + (3 * 3n + n * 3n) + n2(3 + n))(4 + n) = 0 n(6 + 2n + (9n + 3n2) + n2(3 + n))(4 + n) = 0 n(6 + 2n + 9n + 3n2 + (3 * n2 + n * n2))(4 + n) = 0 n(6 + 2n + 9n + 3n2 + (3n2 + n3))(4 + n) = 0 Combine like terms: 2n + 9n = 11n n(6 + 11n + 3n2 + 3n2 + n3)(4 + n) = 0 Combine like terms: 3n2 + 3n2 = 6n2 n(6 + 11n + 6n2 + n3)(4 + n) = 0 Multiply (6 + 11n + 6n2 + n3) * (4 + n) n(6(4 + n) + 11n * (4 + n) + 6n2 * (4 + n) + n3(4 + n)) = 0 n((4 * 6 + n * 6) + 11n * (4 + n) + 6n2 * (4 + n) + n3(4 + n)) = 0 n((24 + 6n) + 11n * (4 + n) + 6n2 * (4 + n) + n3(4 + n)) = 0 n(24 + 6n + (4 * 11n + n * 11n) + 6n2 * (4 + n) + n3(4 + n)) = 0 n(24 + 6n + (44n + 11n2) + 6n2 * (4 + n) + n3(4 + n)) = 0 n(24 + 6n + 44n + 11n2 + (4 * 6n2 + n * 6n2) + n3(4 + n)) = 0 n(24 + 6n + 44n + 11n2 + (24n2 + 6n3) + n3(4 + n)) = 0 n(24 + 6n + 44n + 11n2 + 24n2 + 6n3 + (4 * n3 + n * n3)) = 0 n(24 + 6n + 44n + 11n2 + 24n2 + 6n3 + (4n3 + n4)) = 0 Combine like terms: 6n + 44n = 50n n(24 + 50n + 11n2 + 24n2 + 6n3 + 4n3 + n4) = 0 Combine like terms: 11n2 + 24n2 = 35n2 n(24 + 50n + 35n2 + 6n3 + 4n3 + n4) = 0 Combine like terms: 6n3 + 4n3 = 10n3 n(24 + 50n + 35n2 + 10n3 + n4) = 0 (24 * n + 50n * n + 35n2 * n + 10n3 * n + n4 * n) = 0 (24n + 50n2 + 35n3 + 10n4 + n5) = 0 Solving 24n + 50n2 + 35n3 + 10n4 + n5 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(24 + 50n + 35n2 + 10n3 + n4) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(24 + 50n + 35n2 + 10n3 + n4)' equal to zero and attempt to solve: Simplifying 24 + 50n + 35n2 + 10n3 + n4 = 0 Solving 24 + 50n + 35n2 + 10n3 + n4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
n = {0}
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