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Simplifying 3n2 = -24 + -18n Solving 3n2 = -24 + -18n Solving for variable 'n'. Reorder the terms: 24 + 18n + 3n2 = -24 + -18n + 24 + 18n Reorder the terms: 24 + 18n + 3n2 = -24 + 24 + -18n + 18n Combine like terms: -24 + 24 = 0 24 + 18n + 3n2 = 0 + -18n + 18n 24 + 18n + 3n2 = -18n + 18n Combine like terms: -18n + 18n = 0 24 + 18n + 3n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(8 + 6n + n2) = 0 Factor a trinomial. 3((4 + n)(2 + n)) = 0 Ignore the factor 3.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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