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Simplifying (4x + 12)(3x + 12) = 0 Reorder the terms: (12 + 4x)(3x + 12) = 0 Reorder the terms: (12 + 4x)(12 + 3x) = 0 Multiply (12 + 4x) * (12 + 3x) (12(12 + 3x) + 4x * (12 + 3x)) = 0 ((12 * 12 + 3x * 12) + 4x * (12 + 3x)) = 0 ((144 + 36x) + 4x * (12 + 3x)) = 0 (144 + 36x + (12 * 4x + 3x * 4x)) = 0 (144 + 36x + (48x + 12x2)) = 0 Combine like terms: 36x + 48x = 84x (144 + 84x + 12x2) = 0 Solving 144 + 84x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(12 + 7x + x2) = 0 Factor a trinomial. 12((4 + x)(3 + x)) = 0 Ignore the factor 12.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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {-4, -3}
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