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Simplifying (8n + 5)(n + -4) = 0 Reorder the terms: (5 + 8n)(n + -4) = 0 Reorder the terms: (5 + 8n)(-4 + n) = 0 Multiply (5 + 8n) * (-4 + n) (5(-4 + n) + 8n * (-4 + n)) = 0 ((-4 * 5 + n * 5) + 8n * (-4 + n)) = 0 ((-20 + 5n) + 8n * (-4 + n)) = 0 (-20 + 5n + (-4 * 8n + n * 8n)) = 0 (-20 + 5n + (-32n + 8n2)) = 0 Combine like terms: 5n + -32n = -27n (-20 + -27n + 8n2) = 0 Solving -20 + -27n + 8n2 = 0 Solving for variable 'n'. Factor a trinomial. (-5 + -8n)(4 + -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 '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4Solution
n = {-0.625, 4}
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