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Simplifying 2n2 + 12n + 9 = -7 Reorder the terms: 9 + 12n + 2n2 = -7 Solving 9 + 12n + 2n2 = -7 Solving for variable 'n'. Reorder the terms: 9 + 7 + 12n + 2n2 = -7 + 7 Combine like terms: 9 + 7 = 16 16 + 12n + 2n2 = -7 + 7 Combine like terms: -7 + 7 = 0 16 + 12n + 2n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(8 + 6n + n2) = 0 Factor a trinomial. 2((4 + n)(2 + n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + n)' equal to zero and attempt to solve: Simplifying 4 + n = 0 Solving 4 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + n = 0 + -4 n = 0 + -4 Combine like terms: 0 + -4 = -4 n = -4 Simplifying n = -4Subproblem 2
Set the factor '(2 + n)' equal to zero and attempt to solve: Simplifying 2 + n = 0 Solving 2 + n = 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 + n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + n = 0 + -2 n = 0 + -2 Combine like terms: 0 + -2 = -2 n = -2 Simplifying n = -2Solution
n = {-4, -2}
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