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Simplifying (5n + -4)(2n + -8) = 0 Reorder the terms: (-4 + 5n)(2n + -8) = 0 Reorder the terms: (-4 + 5n)(-8 + 2n) = 0 Multiply (-4 + 5n) * (-8 + 2n) (-4(-8 + 2n) + 5n * (-8 + 2n)) = 0 ((-8 * -4 + 2n * -4) + 5n * (-8 + 2n)) = 0 ((32 + -8n) + 5n * (-8 + 2n)) = 0 (32 + -8n + (-8 * 5n + 2n * 5n)) = 0 (32 + -8n + (-40n + 10n2)) = 0 Combine like terms: -8n + -40n = -48n (32 + -48n + 10n2) = 0 Solving 32 + -48n + 10n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(16 + -24n + 5n2) = 0 Factor a trinomial. 2((4 + -5n)(4 + -1n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -5n)' equal to zero and attempt to solve: Simplifying 4 + -5n = 0 Solving 4 + -5n = 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 + -5n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5n = 0 + -4 -5n = 0 + -4 Combine like terms: 0 + -4 = -4 -5n = -4 Divide each side by '-5'. n = 0.8 Simplifying n = 0.8Subproblem 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 = {0.8, 4}
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