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Simplifying 2(n + 3)(n + 2) + -4(n + 3) = 0 Reorder the terms: 2(3 + n)(n + 2) + -4(n + 3) = 0 Reorder the terms: 2(3 + n)(2 + n) + -4(n + 3) = 0 Multiply (3 + n) * (2 + n) 2(3(2 + n) + n(2 + n)) + -4(n + 3) = 0 2((2 * 3 + n * 3) + n(2 + n)) + -4(n + 3) = 0 2((6 + 3n) + n(2 + n)) + -4(n + 3) = 0 2(6 + 3n + (2 * n + n * n)) + -4(n + 3) = 0 2(6 + 3n + (2n + n2)) + -4(n + 3) = 0 Combine like terms: 3n + 2n = 5n 2(6 + 5n + n2) + -4(n + 3) = 0 (6 * 2 + 5n * 2 + n2 * 2) + -4(n + 3) = 0 (12 + 10n + 2n2) + -4(n + 3) = 0 Reorder the terms: 12 + 10n + 2n2 + -4(3 + n) = 0 12 + 10n + 2n2 + (3 * -4 + n * -4) = 0 12 + 10n + 2n2 + (-12 + -4n) = 0 Reorder the terms: 12 + -12 + 10n + -4n + 2n2 = 0 Combine like terms: 12 + -12 = 0 0 + 10n + -4n + 2n2 = 0 10n + -4n + 2n2 = 0 Combine like terms: 10n + -4n = 6n 6n + 2n2 = 0 Solving 6n + 2n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2n'. 2n(3 + n) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 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 = {0, -3}
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