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Simplifying (n * n * n) + -1n = (n + -1) + n + (n + 1) Multiply n * n (n2 * n) + -1n = (n + -1) + n + (n + 1) Multiply n2 * n (n3) + -1n = (n + -1) + n + (n + 1) n3 + -1n = (n + -1) + n + (n + 1) Reorder the terms: -1n + n3 = (n + -1) + n + (n + 1) Reorder the terms: -1n + n3 = (-1 + n) + n + (n + 1) Remove parenthesis around (-1 + n) -1n + n3 = -1 + n + n + (n + 1) Reorder the terms: -1n + n3 = -1 + n + n + (1 + n) Remove parenthesis around (1 + n) -1n + n3 = -1 + n + n + 1 + n Reorder the terms: -1n + n3 = -1 + 1 + n + n + n Combine like terms: -1 + 1 = 0 -1n + n3 = 0 + n + n + n -1n + n3 = n + n + n Combine like terms: n + n = 2n -1n + n3 = 2n + n Combine like terms: 2n + n = 3n -1n + n3 = 3n Solving -1n + n3 = 3n Solving for variable 'n'. Reorder the terms: -1n + -3n + n3 = 3n + -3n Combine like terms: -1n + -3n = -4n -4n + n3 = 3n + -3n Combine like terms: 3n + -3n = 0 -4n + n3 = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-4 + n2) = 0 Factor a difference between two squares. n((2 + n)(-2 + n)) = 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 '(2 + n)' equal to zero and attempt to solve: Simplifying 2 + n = 0 Solving 2 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + n = 0 + -2 n = 0 + -2 Combine like terms: 0 + -2 = -2 n = -2 Simplifying n = -2Subproblem 3
Set the factor '(-2 + n)' equal to zero and attempt to solve: Simplifying -2 + n = 0 Solving -2 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + n = 0 + 2 n = 0 + 2 Combine like terms: 0 + 2 = 2 n = 2 Simplifying n = 2Solution
n = {0, -2, 2}
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