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Simplifying 6n2 + 69n + 168 = 0 Reorder the terms: 168 + 69n + 6n2 = 0 Solving 168 + 69n + 6n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(56 + 23n + 2n2) = 0 Factor a trinomial. 3((8 + n)(7 + 2n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(8 + n)' equal to zero and attempt to solve: Simplifying 8 + n = 0 Solving 8 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + n = 0 + -8 n = 0 + -8 Combine like terms: 0 + -8 = -8 n = -8 Simplifying n = -8Subproblem 2
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 = -3.5Solution
n = {-8, -3.5}
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