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Simplifying 8n2 + 68n = -84 Reorder the terms: 68n + 8n2 = -84 Solving 68n + 8n2 = -84 Solving for variable 'n'. Reorder the terms: 84 + 68n + 8n2 = -84 + 84 Combine like terms: -84 + 84 = 0 84 + 68n + 8n2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(21 + 17n + 2n2) = 0 Factor a trinomial. 4((7 + n)(3 + 2n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(7 + n)' equal to zero and attempt to solve: Simplifying 7 + n = 0 Solving 7 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + n = 0 + -7 n = 0 + -7 Combine like terms: 0 + -7 = -7 n = -7 Simplifying n = -7Subproblem 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 = {-7, -1.5}
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