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Simplifying 0 = 4x3 + -32x2 + 64x Reorder the terms: 0 = 64x + -32x2 + 4x3 Solving 0 = 64x + -32x2 + 4x3 Solving for variable 'x'. Remove the zero: -64x + 32x2 + -4x3 = 64x + -32x2 + 4x3 + -64x + 32x2 + -4x3 Reorder the terms: -64x + 32x2 + -4x3 = 64x + -64x + -32x2 + 32x2 + 4x3 + -4x3 Combine like terms: 64x + -64x = 0 -64x + 32x2 + -4x3 = 0 + -32x2 + 32x2 + 4x3 + -4x3 -64x + 32x2 + -4x3 = -32x2 + 32x2 + 4x3 + -4x3 Combine like terms: -32x2 + 32x2 = 0 -64x + 32x2 + -4x3 = 0 + 4x3 + -4x3 -64x + 32x2 + -4x3 = 4x3 + -4x3 Combine like terms: 4x3 + -4x3 = 0 -64x + 32x2 + -4x3 = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(-16 + 8x + -1x2) = 0 Factor a trinomial. 4x((-4 + x)(4 + -1x)) = 0 Ignore the factor 4.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 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 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 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Simplifying x = 4Subproblem 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, 4, 4}
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