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Simplifying -4n2 = 18n + 18 Reorder the terms: -4n2 = 18 + 18n Solving -4n2 = 18 + 18n Solving for variable 'n'. Reorder the terms: -18 + -18n + -4n2 = 18 + 18n + -18 + -18n Reorder the terms: -18 + -18n + -4n2 = 18 + -18 + 18n + -18n Combine like terms: 18 + -18 = 0 -18 + -18n + -4n2 = 0 + 18n + -18n -18 + -18n + -4n2 = 18n + -18n Combine like terms: 18n + -18n = 0 -18 + -18n + -4n2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(9 + 9n + 2n2) = 0 Factor a trinomial. -2((3 + n)(3 + 2n)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(3 + n)' equal to zero and attempt to solve: Simplifying 3 + n = 0 Solving 3 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + n = 0 + -3 n = 0 + -3 Combine like terms: 0 + -3 = -3 n = -3 Simplifying n = -3Subproblem 2
Set the factor '(3 + 2n)' equal to zero and attempt to solve: Simplifying 3 + 2n = 0 Solving 3 + 2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2n = 0 + -3 2n = 0 + -3 Combine like terms: 0 + -3 = -3 2n = -3 Divide each side by '2'. n = -1.5 Simplifying n = -1.5Solution
n = {-3, -1.5}
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