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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. (-4 + -1n)(5 + -8n) = 0Subproblem 1
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 = -4Subproblem 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 = {-4, 0.625}
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