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Simplifying (6n + 8)(n + 5) = 0 Reorder the terms: (8 + 6n)(n + 5) = 0 Reorder the terms: (8 + 6n)(5 + n) = 0 Multiply (8 + 6n) * (5 + n) (8(5 + n) + 6n * (5 + n)) = 0 ((5 * 8 + n * 8) + 6n * (5 + n)) = 0 ((40 + 8n) + 6n * (5 + n)) = 0 (40 + 8n + (5 * 6n + n * 6n)) = 0 (40 + 8n + (30n + 6n2)) = 0 Combine like terms: 8n + 30n = 38n (40 + 38n + 6n2) = 0 Solving 40 + 38n + 6n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(20 + 19n + 3n2) = 0 Factor a trinomial. 2((5 + n)(4 + 3n)) = 0 Ignore the factor 2.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 + 3n)' equal to zero and attempt to solve: Simplifying 4 + 3n = 0 Solving 4 + 3n = 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 + 3n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3n = 0 + -4 3n = 0 + -4 Combine like terms: 0 + -4 = -4 3n = -4 Divide each side by '3'. n = -1.333333333 Simplifying n = -1.333333333Solution
n = {-5, -1.333333333}
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