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Simplifying 4n2 + 8n = 96 Reorder the terms: 8n + 4n2 = 96 Solving 8n + 4n2 = 96 Solving for variable 'n'. Reorder the terms: -96 + 8n + 4n2 = 96 + -96 Combine like terms: 96 + -96 = 0 -96 + 8n + 4n2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-24 + 2n + n2) = 0 Factor a trinomial. 4((-6 + -1n)(4 + -1n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve: Simplifying -6 + -1n = 0 Solving -6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1n = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1n = 0 + 6 -1n = 0 + 6 Combine like terms: 0 + 6 = 6 -1n = 6 Divide each side by '-1'. n = -6 Simplifying n = -6Subproblem 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 = {-6, 4}
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