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Simplifying 2(2x + 2)(3x + 6) = 0 Reorder the terms: 2(2 + 2x)(3x + 6) = 0 Reorder the terms: 2(2 + 2x)(6 + 3x) = 0 Multiply (2 + 2x) * (6 + 3x) 2(2(6 + 3x) + 2x * (6 + 3x)) = 0 2((6 * 2 + 3x * 2) + 2x * (6 + 3x)) = 0 2((12 + 6x) + 2x * (6 + 3x)) = 0 2(12 + 6x + (6 * 2x + 3x * 2x)) = 0 2(12 + 6x + (12x + 6x2)) = 0 Combine like terms: 6x + 12x = 18x 2(12 + 18x + 6x2) = 0 (12 * 2 + 18x * 2 + 6x2 * 2) = 0 (24 + 36x + 12x2) = 0 Solving 24 + 36x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(2 + 3x + x2) = 0 Factor a trinomial. 12((2 + x)(1 + 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {-2, -1}
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