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Simplifying (3x + 6)(2x + 8) = 0 Reorder the terms: (6 + 3x)(2x + 8) = 0 Reorder the terms: (6 + 3x)(8 + 2x) = 0 Multiply (6 + 3x) * (8 + 2x) (6(8 + 2x) + 3x * (8 + 2x)) = 0 ((8 * 6 + 2x * 6) + 3x * (8 + 2x)) = 0 ((48 + 12x) + 3x * (8 + 2x)) = 0 (48 + 12x + (8 * 3x + 2x * 3x)) = 0 (48 + 12x + (24x + 6x2)) = 0 Combine like terms: 12x + 24x = 36x (48 + 36x + 6x2) = 0 Solving 48 + 36x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(8 + 6x + x2) = 0 Factor a trinomial. 6((4 + x)(2 + x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-4, -2}
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