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Simplifying x3 + -6x2 + 8x = x2 + -4x Reorder the terms: 8x + -6x2 + x3 = x2 + -4x Reorder the terms: 8x + -6x2 + x3 = -4x + x2 Solving 8x + -6x2 + x3 = -4x + x2 Solving for variable 'x'. Reorder the terms: 8x + 4x + -6x2 + -1x2 + x3 = -4x + x2 + 4x + -1x2 Combine like terms: 8x + 4x = 12x 12x + -6x2 + -1x2 + x3 = -4x + x2 + 4x + -1x2 Combine like terms: -6x2 + -1x2 = -7x2 12x + -7x2 + x3 = -4x + x2 + 4x + -1x2 Reorder the terms: 12x + -7x2 + x3 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 12x + -7x2 + x3 = 0 + x2 + -1x2 12x + -7x2 + x3 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 12x + -7x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(12 + -7x + x2) = 0 Factor a trinomial. x((3 + -1x)(4 + -1x)) = 0Subproblem 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 + -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 = 3Subproblem 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, 3, 4}
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