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Simplifying n3 + -1n2 = 6n Reorder the terms: -1n2 + n3 = 6n Solving -1n2 + n3 = 6n Solving for variable 'n'. Reorder the terms: -6n + -1n2 + n3 = 6n + -6n Combine like terms: 6n + -6n = 0 -6n + -1n2 + n3 = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-6 + -1n + n2) = 0 Factor a trinomial. n((-2 + -1n)(3 + -1n)) = 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 + -1n)' equal to zero and attempt to solve: Simplifying -2 + -1n = 0 Solving -2 + -1n = 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 + -1n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1n = 0 + 2 -1n = 0 + 2 Combine like terms: 0 + 2 = 2 -1n = 2 Divide each side by '-1'. n = -2 Simplifying n = -2Subproblem 3
Set the factor '(3 + -1n)' equal to zero and attempt to solve: Simplifying 3 + -1n = 0 Solving 3 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1n = 0 + -3 -1n = 0 + -3 Combine like terms: 0 + -3 = -3 -1n = -3 Divide each side by '-1'. n = 3 Simplifying n = 3Solution
n = {0, -2, 3}
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