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