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Simplifying 32 + 124n = -112n2 + 4n Reorder the terms: 32 + 124n = 4n + -112n2 Solving 32 + 124n = 4n + -112n2 Solving for variable 'n'. Combine like terms: 124n + -4n = 120n 32 + 120n + 112n2 = 4n + -112n2 + -4n + 112n2 Reorder the terms: 32 + 120n + 112n2 = 4n + -4n + -112n2 + 112n2 Combine like terms: 4n + -4n = 0 32 + 120n + 112n2 = 0 + -112n2 + 112n2 32 + 120n + 112n2 = -112n2 + 112n2 Combine like terms: -112n2 + 112n2 = 0 32 + 120n + 112n2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(4 + 15n + 14n2) = 0 Factor a trinomial. 8((4 + 7n)(1 + 2n)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(4 + 7n)' equal to zero and attempt to solve: Simplifying 4 + 7n = 0 Solving 4 + 7n = 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 + 7n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 7n = 0 + -4 7n = 0 + -4 Combine like terms: 0 + -4 = -4 7n = -4 Divide each side by '7'. n = -0.5714285714 Simplifying n = -0.5714285714Subproblem 2
Set the factor '(1 + 2n)' equal to zero and attempt to solve: Simplifying 1 + 2n = 0 Solving 1 + 2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2n = 0 + -1 2n = 0 + -1 Combine like terms: 0 + -1 = -1 2n = -1 Divide each side by '2'. n = -0.5 Simplifying n = -0.5Solution
n = {-0.5714285714, -0.5}
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