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Simplifying (8n + 5)(n + 7) = 0 Reorder the terms: (5 + 8n)(n + 7) = 0 Reorder the terms: (5 + 8n)(7 + n) = 0 Multiply (5 + 8n) * (7 + n) (5(7 + n) + 8n * (7 + n)) = 0 ((7 * 5 + n * 5) + 8n * (7 + n)) = 0 ((35 + 5n) + 8n * (7 + n)) = 0 (35 + 5n + (7 * 8n + n * 8n)) = 0 (35 + 5n + (56n + 8n2)) = 0 Combine like terms: 5n + 56n = 61n (35 + 61n + 8n2) = 0 Solving 35 + 61n + 8n2 = 0 Solving for variable 'n'. Factor a trinomial. (7 + n)(5 + 8n) = 0Subproblem 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 '(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 = {-7, -0.625}
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