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Simplifying (n + 8)(4n + -5) = 0 Reorder the terms: (8 + n)(4n + -5) = 0 Reorder the terms: (8 + n)(-5 + 4n) = 0 Multiply (8 + n) * (-5 + 4n) (8(-5 + 4n) + n(-5 + 4n)) = 0 ((-5 * 8 + 4n * 8) + n(-5 + 4n)) = 0 ((-40 + 32n) + n(-5 + 4n)) = 0 (-40 + 32n + (-5 * n + 4n * n)) = 0 (-40 + 32n + (-5n + 4n2)) = 0 Combine like terms: 32n + -5n = 27n (-40 + 27n + 4n2) = 0 Solving -40 + 27n + 4n2 = 0 Solving for variable 'n'. Factor a trinomial. (-8 + -1n)(5 + -4n) = 0Subproblem 1
Set the factor '(-8 + -1n)' equal to zero and attempt to solve: Simplifying -8 + -1n = 0 Solving -8 + -1n = 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 + -1n = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1n = 0 + 8 -1n = 0 + 8 Combine like terms: 0 + 8 = 8 -1n = 8 Divide each side by '-1'. n = -8 Simplifying n = -8Subproblem 2
Set the factor '(5 + -4n)' equal to zero and attempt to solve: Simplifying 5 + -4n = 0 Solving 5 + -4n = 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 + -4n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4n = 0 + -5 -4n = 0 + -5 Combine like terms: 0 + -5 = -5 -4n = -5 Divide each side by '-4'. n = 1.25 Simplifying n = 1.25Solution
n = {-8, 1.25}
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