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Simplifying (2x + 3)(2x + 4) = 0 Reorder the terms: (3 + 2x)(2x + 4) = 0 Reorder the terms: (3 + 2x)(4 + 2x) = 0 Multiply (3 + 2x) * (4 + 2x) (3(4 + 2x) + 2x * (4 + 2x)) = 0 ((4 * 3 + 2x * 3) + 2x * (4 + 2x)) = 0 ((12 + 6x) + 2x * (4 + 2x)) = 0 (12 + 6x + (4 * 2x + 2x * 2x)) = 0 (12 + 6x + (8x + 4x2)) = 0 Combine like terms: 6x + 8x = 14x (12 + 14x + 4x2) = 0 Solving 12 + 14x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + 7x + 2x2) = 0 Factor a trinomial. 2((2 + x)(3 + 2x)) = 0 Ignore the factor 2.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 '(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 = {-2, -1.5}
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