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Simplifying 20x3 = -32x2 + 16x Reorder the terms: 20x3 = 16x + -32x2 Solving 20x3 = 16x + -32x2 Solving for variable 'x'. Reorder the terms: -16x + 32x2 + 20x3 = 16x + -32x2 + -16x + 32x2 Reorder the terms: -16x + 32x2 + 20x3 = 16x + -16x + -32x2 + 32x2 Combine like terms: 16x + -16x = 0 -16x + 32x2 + 20x3 = 0 + -32x2 + 32x2 -16x + 32x2 + 20x3 = -32x2 + 32x2 Combine like terms: -32x2 + 32x2 = 0 -16x + 32x2 + 20x3 = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(-4 + 8x + 5x2) = 0 Factor a trinomial. 4x((-2 + -1x)(2 + -5x)) = 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 '(-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 '(2 + -5x)' equal to zero and attempt to solve: Simplifying 2 + -5x = 0 Solving 2 + -5x = 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 + -5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5x = 0 + -2 -5x = 0 + -2 Combine like terms: 0 + -2 = -2 -5x = -2 Divide each side by '-5'. x = 0.4 Simplifying x = 0.4Solution
x = {0, -2, 0.4}
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