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Simplifying 816 = 20n + 4n2 Solving 816 = 20n + 4n2 Solving for variable 'n'. Reorder the terms: 816 + -20n + -4n2 = 20n + -20n + 4n2 + -4n2 Combine like terms: 20n + -20n = 0 816 + -20n + -4n2 = 0 + 4n2 + -4n2 816 + -20n + -4n2 = 4n2 + -4n2 Combine like terms: 4n2 + -4n2 = 0 816 + -20n + -4n2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(204 + -5n + -1n2) = 0 Factor a trinomial. 4((12 + -1n)(17 + n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(12 + -1n)' equal to zero and attempt to solve: Simplifying 12 + -1n = 0 Solving 12 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1n = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1n = 0 + -12 -1n = 0 + -12 Combine like terms: 0 + -12 = -12 -1n = -12 Divide each side by '-1'. n = 12 Simplifying n = 12Subproblem 2
Set the factor '(17 + n)' equal to zero and attempt to solve: Simplifying 17 + n = 0 Solving 17 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + n = 0 + -17 Combine like terms: 17 + -17 = 0 0 + n = 0 + -17 n = 0 + -17 Combine like terms: 0 + -17 = -17 n = -17 Simplifying n = -17Solution
n = {12, -17}
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