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Simplifying x(4x + -3)(2x + -2) = 0 Reorder the terms: x(-3 + 4x)(2x + -2) = 0 Reorder the terms: x(-3 + 4x)(-2 + 2x) = 0 Multiply (-3 + 4x) * (-2 + 2x) x(-3(-2 + 2x) + 4x * (-2 + 2x)) = 0 x((-2 * -3 + 2x * -3) + 4x * (-2 + 2x)) = 0 x((6 + -6x) + 4x * (-2 + 2x)) = 0 x(6 + -6x + (-2 * 4x + 2x * 4x)) = 0 x(6 + -6x + (-8x + 8x2)) = 0 Combine like terms: -6x + -8x = -14x x(6 + -14x + 8x2) = 0 (6 * x + -14x * x + 8x2 * x) = 0 (6x + -14x2 + 8x3) = 0 Solving 6x + -14x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(3 + -7x + 4x2) = 0 Factor a trinomial. 2x((3 + -4x)(1 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 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 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {0, 0.75, 1}
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