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Simplifying (4x + 6)(2x + 6) = 0 Reorder the terms: (6 + 4x)(2x + 6) = 0 Reorder the terms: (6 + 4x)(6 + 2x) = 0 Multiply (6 + 4x) * (6 + 2x) (6(6 + 2x) + 4x * (6 + 2x)) = 0 ((6 * 6 + 2x * 6) + 4x * (6 + 2x)) = 0 ((36 + 12x) + 4x * (6 + 2x)) = 0 (36 + 12x + (6 * 4x + 2x * 4x)) = 0 (36 + 12x + (24x + 8x2)) = 0 Combine like terms: 12x + 24x = 36x (36 + 36x + 8x2) = 0 Solving 36 + 36x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(9 + 9x + 2x2) = 0 Factor a trinomial. 4((3 + x)(3 + 2x)) = 0 Ignore the factor 4.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 '(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 = {-3, -1.5}
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