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Simplifying 12n2 + 87n + 135 = 0 Reorder the terms: 135 + 87n + 12n2 = 0 Solving 135 + 87n + 12n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(45 + 29n + 4n2) = 0 Factor a trinomial. 3((5 + n)(9 + 4n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + n)' equal to zero and attempt to solve: Simplifying 5 + n = 0 Solving 5 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + n = 0 + -5 n = 0 + -5 Combine like terms: 0 + -5 = -5 n = -5 Simplifying n = -5Subproblem 2
Set the factor '(9 + 4n)' equal to zero and attempt to solve: Simplifying 9 + 4n = 0 Solving 9 + 4n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 4n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4n = 0 + -9 4n = 0 + -9 Combine like terms: 0 + -9 = -9 4n = -9 Divide each side by '4'. n = -2.25 Simplifying n = -2.25Solution
n = {-5, -2.25}
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