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Simplifying (3 + -2x)(4 + -2x) * x = 0 Reorder the terms for easier multiplication: x(3 + -2x)(4 + -2x) = 0 Multiply (3 + -2x) * (4 + -2x) x(3(4 + -2x) + -2x * (4 + -2x)) = 0 x((4 * 3 + -2x * 3) + -2x * (4 + -2x)) = 0 x((12 + -6x) + -2x * (4 + -2x)) = 0 x(12 + -6x + (4 * -2x + -2x * -2x)) = 0 x(12 + -6x + (-8x + 4x2)) = 0 Combine like terms: -6x + -8x = -14x x(12 + -14x + 4x2) = 0 (12 * x + -14x * x + 4x2 * x) = 0 (12x + -14x2 + 4x3) = 0 Solving 12x + -14x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(6 + -7x + 2x2) = 0 Factor a trinomial. 2x((3 + -2x)(2 + -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 + -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 = 1.5Subproblem 3
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 = 2Solution
x = {0, 1.5, 2}
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