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Simplifying (n + 8)(8n + 5) = 0 Reorder the terms: (8 + n)(8n + 5) = 0 Reorder the terms: (8 + n)(5 + 8n) = 0 Multiply (8 + n) * (5 + 8n) (8(5 + 8n) + n(5 + 8n)) = 0 ((5 * 8 + 8n * 8) + n(5 + 8n)) = 0 ((40 + 64n) + n(5 + 8n)) = 0 (40 + 64n + (5 * n + 8n * n)) = 0 (40 + 64n + (5n + 8n2)) = 0 Combine like terms: 64n + 5n = 69n (40 + 69n + 8n2) = 0 Solving 40 + 69n + 8n2 = 0 Solving for variable 'n'. Factor a trinomial. (8 + n)(5 + 8n) = 0Subproblem 1
Set the factor '(8 + n)' equal to zero and attempt to solve: Simplifying 8 + n = 0 Solving 8 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + n = 0 + -8 n = 0 + -8 Combine like terms: 0 + -8 = -8 n = -8 Simplifying n = -8Subproblem 2
Set the factor '(5 + 8n)' equal to zero and attempt to solve: Simplifying 5 + 8n = 0 Solving 5 + 8n = 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 + 8n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 8n = 0 + -5 8n = 0 + -5 Combine like terms: 0 + -5 = -5 8n = -5 Divide each side by '8'. n = -0.625 Simplifying n = -0.625Solution
n = {-8, -0.625}
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