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Simplifying 27n2 + 156n + 105 = 0 Reorder the terms: 105 + 156n + 27n2 = 0 Solving 105 + 156n + 27n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(35 + 52n + 9n2) = 0 Factor a trinomial. 3((5 + n)(7 + 9n)) = 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 '(7 + 9n)' equal to zero and attempt to solve: Simplifying 7 + 9n = 0 Solving 7 + 9n = 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 + 9n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 9n = 0 + -7 9n = 0 + -7 Combine like terms: 0 + -7 = -7 9n = -7 Divide each side by '9'. n = -0.7777777778 Simplifying n = -0.7777777778Solution
n = {-5, -0.7777777778}
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