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Simplifying 4(2x + -3) + 2x(2x + -3) = 0 Reorder the terms: 4(-3 + 2x) + 2x(2x + -3) = 0 (-3 * 4 + 2x * 4) + 2x(2x + -3) = 0 (-12 + 8x) + 2x(2x + -3) = 0 Reorder the terms: -12 + 8x + 2x(-3 + 2x) = 0 -12 + 8x + (-3 * 2x + 2x * 2x) = 0 -12 + 8x + (-6x + 4x2) = 0 Combine like terms: 8x + -6x = 2x -12 + 2x + 4x2 = 0 Solving -12 + 2x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + x + 2x2) = 0 Factor a trinomial. 2((-2 + -1x)(3 + -2x)) = 0 Ignore the factor 2.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 + -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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