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Simplifying (n + 4)(6n + 8) = 0 Reorder the terms: (4 + n)(6n + 8) = 0 Reorder the terms: (4 + n)(8 + 6n) = 0 Multiply (4 + n) * (8 + 6n) (4(8 + 6n) + n(8 + 6n)) = 0 ((8 * 4 + 6n * 4) + n(8 + 6n)) = 0 ((32 + 24n) + n(8 + 6n)) = 0 (32 + 24n + (8 * n + 6n * n)) = 0 (32 + 24n + (8n + 6n2)) = 0 Combine like terms: 24n + 8n = 32n (32 + 32n + 6n2) = 0 Solving 32 + 32n + 6n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(16 + 16n + 3n2) = 0 Factor a trinomial. 2((4 + n)(4 + 3n)) = 0 Ignore the factor 2.Subproblem 1
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 = -4Subproblem 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 = {-4, -1.333333333}
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