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Simplifying 280 = 4(n + 2)(n + 5) Reorder the terms: 280 = 4(2 + n)(n + 5) Reorder the terms: 280 = 4(2 + n)(5 + n) Multiply (2 + n) * (5 + n) 280 = 4(2(5 + n) + n(5 + n)) 280 = 4((5 * 2 + n * 2) + n(5 + n)) 280 = 4((10 + 2n) + n(5 + n)) 280 = 4(10 + 2n + (5 * n + n * n)) 280 = 4(10 + 2n + (5n + n2)) Combine like terms: 2n + 5n = 7n 280 = 4(10 + 7n + n2) 280 = (10 * 4 + 7n * 4 + n2 * 4) 280 = (40 + 28n + 4n2) Solving 280 = 40 + 28n + 4n2 Solving for variable 'n'. Combine like terms: 280 + -40 = 240 240 + -28n + -4n2 = 40 + 28n + 4n2 + -40 + -28n + -4n2 Reorder the terms: 240 + -28n + -4n2 = 40 + -40 + 28n + -28n + 4n2 + -4n2 Combine like terms: 40 + -40 = 0 240 + -28n + -4n2 = 0 + 28n + -28n + 4n2 + -4n2 240 + -28n + -4n2 = 28n + -28n + 4n2 + -4n2 Combine like terms: 28n + -28n = 0 240 + -28n + -4n2 = 0 + 4n2 + -4n2 240 + -28n + -4n2 = 4n2 + -4n2 Combine like terms: 4n2 + -4n2 = 0 240 + -28n + -4n2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(60 + -7n + -1n2) = 0 Factor a trinomial. 4((5 + -1n)(12 + n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -1n)' equal to zero and attempt to solve: Simplifying 5 + -1n = 0 Solving 5 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n = 0 + -5 -1n = 0 + -5 Combine like terms: 0 + -5 = -5 -1n = -5 Divide each side by '-1'. n = 5 Simplifying n = 5Subproblem 2
Set the factor '(12 + n)' equal to zero and attempt to solve: Simplifying 12 + n = 0 Solving 12 + n = 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 + n = 0 + -12 Combine like terms: 12 + -12 = 0 0 + n = 0 + -12 n = 0 + -12 Combine like terms: 0 + -12 = -12 n = -12 Simplifying n = -12Solution
n = {5, -12}
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