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Simplifying (n + -5)(3n + -8) = 0 Reorder the terms: (-5 + n)(3n + -8) = 0 Reorder the terms: (-5 + n)(-8 + 3n) = 0 Multiply (-5 + n) * (-8 + 3n) (-5(-8 + 3n) + n(-8 + 3n)) = 0 ((-8 * -5 + 3n * -5) + n(-8 + 3n)) = 0 ((40 + -15n) + n(-8 + 3n)) = 0 (40 + -15n + (-8 * n + 3n * n)) = 0 (40 + -15n + (-8n + 3n2)) = 0 Combine like terms: -15n + -8n = -23n (40 + -23n + 3n2) = 0 Solving 40 + -23n + 3n2 = 0 Solving for variable 'n'. Factor a trinomial. (8 + -3n)(5 + -1n) = 0Subproblem 1
Set the factor '(8 + -3n)' equal to zero and attempt to solve: Simplifying 8 + -3n = 0 Solving 8 + -3n = 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 + -3n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3n = 0 + -8 -3n = 0 + -8 Combine like terms: 0 + -8 = -8 -3n = -8 Divide each side by '-3'. n = 2.666666667 Simplifying n = 2.666666667Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve: Simplifying 5 + -1n = 0 Solving 5 + -1n = 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 + -1n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n = 0 + -5 -1n = 0 + -5 Combine like terms: 0 + -5 = -5 -1n = -5 Divide each side by '-1'. n = 5 Simplifying n = 5Solution
n = {2.666666667, 5}
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