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Simplifying (2x + 4)(6x + 12) = 0 Reorder the terms: (4 + 2x)(6x + 12) = 0 Reorder the terms: (4 + 2x)(12 + 6x) = 0 Multiply (4 + 2x) * (12 + 6x) (4(12 + 6x) + 2x * (12 + 6x)) = 0 ((12 * 4 + 6x * 4) + 2x * (12 + 6x)) = 0 ((48 + 24x) + 2x * (12 + 6x)) = 0 (48 + 24x + (12 * 2x + 6x * 2x)) = 0 (48 + 24x + (24x + 12x2)) = 0 Combine like terms: 24x + 24x = 48x (48 + 48x + 12x2) = 0 Solving 48 + 48x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(4 + 4x + x2) = 0 Factor a trinomial. 12((2 + x)(2 + x)) = 0 Ignore the factor 12.Subproblem 1
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 = -2Subproblem 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 = {-2, -2}
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