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Simplifying 12n3 + -66n2 + -126n = 0 Reorder the terms: -126n + -66n2 + 12n3 = 0 Solving -126n + -66n2 + 12n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '6n'. 6n(-21 + -11n + 2n2) = 0 Factor a trinomial. 6n((-3 + -2n)(7 + -1n)) = 0 Ignore the factor 6.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 '(-3 + -2n)' equal to zero and attempt to solve: Simplifying -3 + -2n = 0 Solving -3 + -2n = 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 + -2n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2n = 0 + 3 -2n = 0 + 3 Combine like terms: 0 + 3 = 3 -2n = 3 Divide each side by '-2'. n = -1.5 Simplifying n = -1.5Subproblem 3
Set the factor '(7 + -1n)' equal to zero and attempt to solve: Simplifying 7 + -1n = 0 Solving 7 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1n = 0 + -7 -1n = 0 + -7 Combine like terms: 0 + -7 = -7 -1n = -7 Divide each side by '-1'. n = 7 Simplifying n = 7Solution
n = {0, -1.5, 7}
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