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Simplifying 2x(3x + -2)(x + 4) = 0 Reorder the terms: 2x(-2 + 3x)(x + 4) = 0 Reorder the terms: 2x(-2 + 3x)(4 + x) = 0 Multiply (-2 + 3x) * (4 + x) 2x(-2(4 + x) + 3x * (4 + x)) = 0 2x((4 * -2 + x * -2) + 3x * (4 + x)) = 0 2x((-8 + -2x) + 3x * (4 + x)) = 0 2x(-8 + -2x + (4 * 3x + x * 3x)) = 0 2x(-8 + -2x + (12x + 3x2)) = 0 Combine like terms: -2x + 12x = 10x 2x(-8 + 10x + 3x2) = 0 (-8 * 2x + 10x * 2x + 3x2 * 2x) = 0 (-16x + 20x2 + 6x3) = 0 Solving -16x + 20x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-8 + 10x + 3x2) = 0 Factor a trinomial. 2x((-4 + -1x)(2 + -3x)) = 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 '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 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 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 3
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 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 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {0, -4, 0.6666666667}
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