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Simplifying (2x + -6)(x + 4) * x = 0 Reorder the terms: (-6 + 2x)(x + 4) * x = 0 Reorder the terms: (-6 + 2x)(4 + x) * x = 0 Reorder the terms for easier multiplication: x(-6 + 2x)(4 + x) = 0 Multiply (-6 + 2x) * (4 + x) x(-6(4 + x) + 2x * (4 + x)) = 0 x((4 * -6 + x * -6) + 2x * (4 + x)) = 0 x((-24 + -6x) + 2x * (4 + x)) = 0 x(-24 + -6x + (4 * 2x + x * 2x)) = 0 x(-24 + -6x + (8x + 2x2)) = 0 Combine like terms: -6x + 8x = 2x x(-24 + 2x + 2x2) = 0 (-24 * x + 2x * x + 2x2 * x) = 0 (-24x + 2x2 + 2x3) = 0 Solving -24x + 2x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-12 + x + x2) = 0 Factor a trinomial. 2x((-4 + -1x)(3 + -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 '(-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 '(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 = {0, -4, 3}
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