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Simplifying (8n + -5)(n + -3) = 0 Reorder the terms: (-5 + 8n)(n + -3) = 0 Reorder the terms: (-5 + 8n)(-3 + n) = 0 Multiply (-5 + 8n) * (-3 + n) (-5(-3 + n) + 8n * (-3 + n)) = 0 ((-3 * -5 + n * -5) + 8n * (-3 + n)) = 0 ((15 + -5n) + 8n * (-3 + n)) = 0 (15 + -5n + (-3 * 8n + n * 8n)) = 0 (15 + -5n + (-24n + 8n2)) = 0 Combine like terms: -5n + -24n = -29n (15 + -29n + 8n2) = 0 Solving 15 + -29n + 8n2 = 0 Solving for variable 'n'. Factor a trinomial. (5 + -8n)(3 + -1n) = 0Subproblem 1
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 = 0.625Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve: Simplifying 3 + -1n = 0 Solving 3 + -1n = 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 + -1n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1n = 0 + -3 -1n = 0 + -3 Combine like terms: 0 + -3 = -3 -1n = -3 Divide each side by '-1'. n = 3 Simplifying n = 3Solution
n = {0.625, 3}
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