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Simplifying 8n2 + 48 = -44n Reorder the terms: 48 + 8n2 = -44n Solving 48 + 8n2 = -44n Solving for variable 'n'. Reorder the terms: 48 + 44n + 8n2 = -44n + 44n Combine like terms: -44n + 44n = 0 48 + 44n + 8n2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(12 + 11n + 2n2) = 0 Factor a trinomial. 4((4 + n)(3 + 2n)) = 0 Ignore the factor 4.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 '(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 = {-4, -1.5}
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