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Simplifying 2n2 + 24n + 72 = 8 Reorder the terms: 72 + 24n + 2n2 = 8 Solving 72 + 24n + 2n2 = 8 Solving for variable 'n'. Reorder the terms: 72 + -8 + 24n + 2n2 = 8 + -8 Combine like terms: 72 + -8 = 64 64 + 24n + 2n2 = 8 + -8 Combine like terms: 8 + -8 = 0 64 + 24n + 2n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(32 + 12n + n2) = 0 Factor a trinomial. 2((8 + n)(4 + n)) = 0 Ignore the factor 2.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 '(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 = -4Solution
n = {-8, -4}
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