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Simplifying 0 = 2x + -32x3 Solving 0 = 2x + -32x3 Solving for variable 'x'. Remove the zero: -2x + 32x3 = 2x + -32x3 + -2x + 32x3 Reorder the terms: -2x + 32x3 = 2x + -2x + -32x3 + 32x3 Combine like terms: 2x + -2x = 0 -2x + 32x3 = 0 + -32x3 + 32x3 -2x + 32x3 = -32x3 + 32x3 Combine like terms: -32x3 + 32x3 = 0 -2x + 32x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(-1 + 16x2) = 0 Factor a difference between two squares. 2x((1 + 4x)(-1 + 4x)) = 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 '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Divide each side by '4'. x = -0.25 Simplifying x = -0.25Subproblem 3
Set the factor '(-1 + 4x)' equal to zero and attempt to solve: Simplifying -1 + 4x = 0 Solving -1 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 4x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4x = 0 + 1 4x = 0 + 1 Combine like terms: 0 + 1 = 1 4x = 1 Divide each side by '4'. x = 0.25 Simplifying x = 0.25Solution
x = {0, -0.25, 0.25}
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