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Simplifying 8(n + 3)(n + 7) = 0 Reorder the terms: 8(3 + n)(n + 7) = 0 Reorder the terms: 8(3 + n)(7 + n) = 0 Multiply (3 + n) * (7 + n) 8(3(7 + n) + n(7 + n)) = 0 8((7 * 3 + n * 3) + n(7 + n)) = 0 8((21 + 3n) + n(7 + n)) = 0 8(21 + 3n + (7 * n + n * n)) = 0 8(21 + 3n + (7n + n2)) = 0 Combine like terms: 3n + 7n = 10n 8(21 + 10n + n2) = 0 (21 * 8 + 10n * 8 + n2 * 8) = 0 (168 + 80n + 8n2) = 0 Solving 168 + 80n + 8n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '8'. 8(21 + 10n + n2) = 0 Factor a trinomial. 8((7 + n)(3 + n)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(7 + n)' equal to zero and attempt to solve: Simplifying 7 + n = 0 Solving 7 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + n = 0 + -7 n = 0 + -7 Combine like terms: 0 + -7 = -7 n = -7 Simplifying n = -7Subproblem 2
Set the factor '(3 + n)' equal to zero and attempt to solve: Simplifying 3 + n = 0 Solving 3 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + n = 0 + -3 n = 0 + -3 Combine like terms: 0 + -3 = -3 n = -3 Simplifying n = -3Solution
n = {-7, -3}
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