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Simplifying 2x3 = 4x2 + 16x Reorder the terms: 2x3 = 16x + 4x2 Solving 2x3 = 16x + 4x2 Solving for variable 'x'. Reorder the terms: -16x + -4x2 + 2x3 = 16x + 4x2 + -16x + -4x2 Reorder the terms: -16x + -4x2 + 2x3 = 16x + -16x + 4x2 + -4x2 Combine like terms: 16x + -16x = 0 -16x + -4x2 + 2x3 = 0 + 4x2 + -4x2 -16x + -4x2 + 2x3 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -16x + -4x2 + 2x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(-8 + -2x + x2) = 0 Factor a trinomial. 2x((-2 + -1x)(4 + -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 '(-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 3
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 = 4Solution
x = {0, -2, 4}
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