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Simplifying n(4n + 8) = 252 Reorder the terms: n(8 + 4n) = 252 (8 * n + 4n * n) = 252 (8n + 4n2) = 252 Solving 8n + 4n2 = 252 Solving for variable 'n'. Reorder the terms: -252 + 8n + 4n2 = 252 + -252 Combine like terms: 252 + -252 = 0 -252 + 8n + 4n2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-63 + 2n + n2) = 0 Factor a trinomial. 4((-9 + -1n)(7 + -1n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9 + -1n)' equal to zero and attempt to solve: Simplifying -9 + -1n = 0 Solving -9 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1n = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1n = 0 + 9 -1n = 0 + 9 Combine like terms: 0 + 9 = 9 -1n = 9 Divide each side by '-1'. n = -9 Simplifying n = -9Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve: Simplifying 7 + -1n = 0 Solving 7 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1n = 0 + -7 -1n = 0 + -7 Combine like terms: 0 + -7 = -7 -1n = -7 Divide each side by '-1'. n = 7 Simplifying n = 7Solution
n = {-9, 7}
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