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Simplifying 4n(n + -4) + -8n(n + 5) = 0 Reorder the terms: 4n(-4 + n) + -8n(n + 5) = 0 (-4 * 4n + n * 4n) + -8n(n + 5) = 0 (-16n + 4n2) + -8n(n + 5) = 0 Reorder the terms: -16n + 4n2 + -8n(5 + n) = 0 -16n + 4n2 + (5 * -8n + n * -8n) = 0 -16n + 4n2 + (-40n + -8n2) = 0 Reorder the terms: -16n + -40n + 4n2 + -8n2 = 0 Combine like terms: -16n + -40n = -56n -56n + 4n2 + -8n2 = 0 Combine like terms: 4n2 + -8n2 = -4n2 -56n + -4n2 = 0 Solving -56n + -4n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '-4n'. -4n(14 + n) = 0 Ignore the factor -4.Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(14 + n)' equal to zero and attempt to solve: Simplifying 14 + n = 0 Solving 14 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + n = 0 + -14 Combine like terms: 14 + -14 = 0 0 + n = 0 + -14 n = 0 + -14 Combine like terms: 0 + -14 = -14 n = -14 Simplifying n = -14Solution
n = {0, -14}
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