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Simplifying (2x + -4)(4x + -12) = 0 Reorder the terms: (-4 + 2x)(4x + -12) = 0 Reorder the terms: (-4 + 2x)(-12 + 4x) = 0 Multiply (-4 + 2x) * (-12 + 4x) (-4(-12 + 4x) + 2x * (-12 + 4x)) = 0 ((-12 * -4 + 4x * -4) + 2x * (-12 + 4x)) = 0 ((48 + -16x) + 2x * (-12 + 4x)) = 0 (48 + -16x + (-12 * 2x + 4x * 2x)) = 0 (48 + -16x + (-24x + 8x2)) = 0 Combine like terms: -16x + -24x = -40x (48 + -40x + 8x2) = 0 Solving 48 + -40x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(6 + -5x + x2) = 0 Factor a trinomial. 8((2 + -1x)(3 + -1x)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {2, 3}
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