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Simplifying 5(n + 4)(n + 5) = 0 Reorder the terms: 5(4 + n)(n + 5) = 0 Reorder the terms: 5(4 + n)(5 + n) = 0 Multiply (4 + n) * (5 + n) 5(4(5 + n) + n(5 + n)) = 0 5((5 * 4 + n * 4) + n(5 + n)) = 0 5((20 + 4n) + n(5 + n)) = 0 5(20 + 4n + (5 * n + n * n)) = 0 5(20 + 4n + (5n + n2)) = 0 Combine like terms: 4n + 5n = 9n 5(20 + 9n + n2) = 0 (20 * 5 + 9n * 5 + n2 * 5) = 0 (100 + 45n + 5n2) = 0 Solving 100 + 45n + 5n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '5'. 5(20 + 9n + n2) = 0 Factor a trinomial. 5((5 + n)(4 + n)) = 0 Ignore the factor 5.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 '(4 + n)' equal to zero and attempt to solve: Simplifying 4 + n = 0 Solving 4 + n = 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 + n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + n = 0 + -4 n = 0 + -4 Combine like terms: 0 + -4 = -4 n = -4 Simplifying n = -4Solution
n = {-5, -4}
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