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Simplifying 12n3 + -4n2 = 8n Reorder the terms: -4n2 + 12n3 = 8n Solving -4n2 + 12n3 = 8n Solving for variable 'n'. Reorder the terms: -8n + -4n2 + 12n3 = 8n + -8n Combine like terms: 8n + -8n = 0 -8n + -4n2 + 12n3 = 0 Factor out the Greatest Common Factor (GCF), '4n'. 4n(-2 + -1n + 3n2) = 0 Factor a trinomial. 4n((-2 + -3n)(1 + -1n)) = 0 Ignore the factor 4.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 '(-2 + -3n)' equal to zero and attempt to solve: Simplifying -2 + -3n = 0 Solving -2 + -3n = 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 + -3n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3n = 0 + 2 -3n = 0 + 2 Combine like terms: 0 + 2 = 2 -3n = 2 Divide each side by '-3'. n = -0.6666666667 Simplifying n = -0.6666666667Subproblem 3
Set the factor '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 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 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1Solution
n = {0, -0.6666666667, 1}
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