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Simplifying (3x + 6)(4x + 2) = 0 Reorder the terms: (6 + 3x)(4x + 2) = 0 Reorder the terms: (6 + 3x)(2 + 4x) = 0 Multiply (6 + 3x) * (2 + 4x) (6(2 + 4x) + 3x * (2 + 4x)) = 0 ((2 * 6 + 4x * 6) + 3x * (2 + 4x)) = 0 ((12 + 24x) + 3x * (2 + 4x)) = 0 (12 + 24x + (2 * 3x + 4x * 3x)) = 0 (12 + 24x + (6x + 12x2)) = 0 Combine like terms: 24x + 6x = 30x (12 + 30x + 12x2) = 0 Solving 12 + 30x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(2 + 5x + 2x2) = 0 Factor a trinomial. 6((2 + x)(1 + 2x)) = 0 Ignore the factor 6.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 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {-2, -0.5}
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