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Simplifying (2x + 4)(3 + x) = 0 Reorder the terms: (4 + 2x)(3 + x) = 0 Multiply (4 + 2x) * (3 + x) (4(3 + x) + 2x * (3 + x)) = 0 ((3 * 4 + x * 4) + 2x * (3 + x)) = 0 ((12 + 4x) + 2x * (3 + x)) = 0 (12 + 4x + (3 * 2x + x * 2x)) = 0 (12 + 4x + (6x + 2x2)) = 0 Combine like terms: 4x + 6x = 10x (12 + 10x + 2x2) = 0 Solving 12 + 10x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + 5x + x2) = 0 Factor a trinomial. 2((3 + x)(2 + x)) = 0 Ignore the factor 2.Subproblem 1
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 = -3Subproblem 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 = {-3, -2}
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