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Simplifying (4x + 12)(2x + 10) = 0 Reorder the terms: (12 + 4x)(2x + 10) = 0 Reorder the terms: (12 + 4x)(10 + 2x) = 0 Multiply (12 + 4x) * (10 + 2x) (12(10 + 2x) + 4x * (10 + 2x)) = 0 ((10 * 12 + 2x * 12) + 4x * (10 + 2x)) = 0 ((120 + 24x) + 4x * (10 + 2x)) = 0 (120 + 24x + (10 * 4x + 2x * 4x)) = 0 (120 + 24x + (40x + 8x2)) = 0 Combine like terms: 24x + 40x = 64x (120 + 64x + 8x2) = 0 Solving 120 + 64x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(15 + 8x + x2) = 0 Factor a trinomial. 8((5 + x)(3 + x)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 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 = {-5, -3}
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