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Simplifying (4x + 6)(2x + 8) = 0 Reorder the terms: (6 + 4x)(2x + 8) = 0 Reorder the terms: (6 + 4x)(8 + 2x) = 0 Multiply (6 + 4x) * (8 + 2x) (6(8 + 2x) + 4x * (8 + 2x)) = 0 ((8 * 6 + 2x * 6) + 4x * (8 + 2x)) = 0 ((48 + 12x) + 4x * (8 + 2x)) = 0 (48 + 12x + (8 * 4x + 2x * 4x)) = 0 (48 + 12x + (32x + 8x2)) = 0 Combine like terms: 12x + 32x = 44x (48 + 44x + 8x2) = 0 Solving 48 + 44x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(12 + 11x + 2x2) = 0 Factor a trinomial. 4((4 + x)(3 + 2x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 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 = {-4, -1.5}
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