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Simplifying 36n2 + 102n + -84 = 0 Reorder the terms: -84 + 102n + 36n2 = 0 Solving -84 + 102n + 36n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '6'. 6(-14 + 17n + 6n2) = 0 Factor a trinomial. 6((-7 + -2n)(2 + -3n)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-7 + -2n)' equal to zero and attempt to solve: Simplifying -7 + -2n = 0 Solving -7 + -2n = 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 + -2n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2n = 0 + 7 -2n = 0 + 7 Combine like terms: 0 + 7 = 7 -2n = 7 Divide each side by '-2'. n = -3.5 Simplifying n = -3.5Subproblem 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 = 0.6666666667Solution
n = {-3.5, 0.6666666667}
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