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Simplifying 2n3 + 5n = 7n Reorder the terms: 5n + 2n3 = 7n Solving 5n + 2n3 = 7n Solving for variable 'n'. Reorder the terms: 5n + -7n + 2n3 = 7n + -7n Combine like terms: 5n + -7n = -2n -2n + 2n3 = 7n + -7n Combine like terms: 7n + -7n = 0 -2n + 2n3 = 0 Factor out the Greatest Common Factor (GCF), '2n'. 2n(-1 + n2) = 0 Factor a difference between two squares. 2n((1 + n)(-1 + n)) = 0 Ignore the factor 2.Subproblem 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 '(1 + n)' equal to zero and attempt to solve: Simplifying 1 + n = 0 Solving 1 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + n = 0 + -1 n = 0 + -1 Combine like terms: 0 + -1 = -1 n = -1 Simplifying n = -1Subproblem 3
Set the factor '(-1 + n)' equal to zero and attempt to solve: Simplifying -1 + n = 0 Solving -1 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + n = 0 + 1 n = 0 + 1 Combine like terms: 0 + 1 = 1 n = 1 Simplifying n = 1Solution
n = {0, -1, 1}
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