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Simplifying -8n(n + 6) = 5 + -7n Reorder the terms: -8n(6 + n) = 5 + -7n (6 * -8n + n * -8n) = 5 + -7n (-48n + -8n2) = 5 + -7n Solving -48n + -8n2 = 5 + -7n Solving for variable 'n'. Reorder the terms: -5 + -48n + 7n + -8n2 = 5 + -7n + -5 + 7n Combine like terms: -48n + 7n = -41n -5 + -41n + -8n2 = 5 + -7n + -5 + 7n Reorder the terms: -5 + -41n + -8n2 = 5 + -5 + -7n + 7n Combine like terms: 5 + -5 = 0 -5 + -41n + -8n2 = 0 + -7n + 7n -5 + -41n + -8n2 = -7n + 7n Combine like terms: -7n + 7n = 0 -5 + -41n + -8n2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 41n + 8n2) = 0 Factor a trinomial. -1((5 + n)(1 + 8n)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + n)' equal to zero and attempt to solve: Simplifying 5 + n = 0 Solving 5 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + n = 0 + -5 n = 0 + -5 Combine like terms: 0 + -5 = -5 n = -5 Simplifying n = -5Subproblem 2
Set the factor '(1 + 8n)' equal to zero and attempt to solve: Simplifying 1 + 8n = 0 Solving 1 + 8n = 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 + 8n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 8n = 0 + -1 8n = 0 + -1 Combine like terms: 0 + -1 = -1 8n = -1 Divide each side by '8'. n = -0.125 Simplifying n = -0.125Solution
n = {-5, -0.125}
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