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Simplifying 0 = 32x3 + -162x Reorder the terms: 0 = -162x + 32x3 Solving 0 = -162x + 32x3 Solving for variable 'x'. Remove the zero: 162x + -32x3 = -162x + 32x3 + 162x + -32x3 Reorder the terms: 162x + -32x3 = -162x + 162x + 32x3 + -32x3 Combine like terms: -162x + 162x = 0 162x + -32x3 = 0 + 32x3 + -32x3 162x + -32x3 = 32x3 + -32x3 Combine like terms: 32x3 + -32x3 = 0 162x + -32x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(81 + -16x2) = 0 Factor a difference between two squares. 2x((9 + 4x)(9 + -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 '(9 + 4x)' equal to zero and attempt to solve: Simplifying 9 + 4x = 0 Solving 9 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 4x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4x = 0 + -9 4x = 0 + -9 Combine like terms: 0 + -9 = -9 4x = -9 Divide each side by '4'. x = -2.25 Simplifying x = -2.25Subproblem 3
Set the factor '(9 + -4x)' equal to zero and attempt to solve: Simplifying 9 + -4x = 0 Solving 9 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -4x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4x = 0 + -9 -4x = 0 + -9 Combine like terms: 0 + -9 = -9 -4x = -9 Divide each side by '-4'. x = 2.25 Simplifying x = 2.25Solution
x = {0, -2.25, 2.25}
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