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Simplifying (2n + 5)(n + -8) = 0 Reorder the terms: (5 + 2n)(n + -8) = 0 Reorder the terms: (5 + 2n)(-8 + n) = 0 Multiply (5 + 2n) * (-8 + n) (5(-8 + n) + 2n * (-8 + n)) = 0 ((-8 * 5 + n * 5) + 2n * (-8 + n)) = 0 ((-40 + 5n) + 2n * (-8 + n)) = 0 (-40 + 5n + (-8 * 2n + n * 2n)) = 0 (-40 + 5n + (-16n + 2n2)) = 0 Combine like terms: 5n + -16n = -11n (-40 + -11n + 2n2) = 0 Solving -40 + -11n + 2n2 = 0 Solving for variable 'n'. Factor a trinomial. (-5 + -2n)(8 + -1n) = 0Subproblem 1
Set the factor '(-5 + -2n)' equal to zero and attempt to solve: Simplifying -5 + -2n = 0 Solving -5 + -2n = 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 + -2n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2n = 0 + 5 -2n = 0 + 5 Combine like terms: 0 + 5 = 5 -2n = 5 Divide each side by '-2'. n = -2.5 Simplifying n = -2.5Subproblem 2
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 = 8Solution
n = {-2.5, 8}
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