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Simplifying (2x + 3)(4x + 6) = 0 Reorder the terms: (3 + 2x)(4x + 6) = 0 Reorder the terms: (3 + 2x)(6 + 4x) = 0 Multiply (3 + 2x) * (6 + 4x) (3(6 + 4x) + 2x * (6 + 4x)) = 0 ((6 * 3 + 4x * 3) + 2x * (6 + 4x)) = 0 ((18 + 12x) + 2x * (6 + 4x)) = 0 (18 + 12x + (6 * 2x + 4x * 2x)) = 0 (18 + 12x + (12x + 8x2)) = 0 Combine like terms: 12x + 12x = 24x (18 + 24x + 8x2) = 0 Solving 18 + 24x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + 12x + 4x2) = 0 Factor a trinomial. 2((3 + 2x)(3 + 2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Solution
x = {-1.5, -1.5}
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