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Simplifying (x5 + -4x3)(8x2 + -32) = 0 Reorder the terms: (-4x3 + x5)(8x2 + -32) = 0 Reorder the terms: (-4x3 + x5)(-32 + 8x2) = 0 Multiply (-4x3 + x5) * (-32 + 8x2) (-4x3 * (-32 + 8x2) + x5(-32 + 8x2)) = 0 ((-32 * -4x3 + 8x2 * -4x3) + x5(-32 + 8x2)) = 0 ((128x3 + -32x5) + x5(-32 + 8x2)) = 0 (128x3 + -32x5 + (-32 * x5 + 8x2 * x5)) = 0 (128x3 + -32x5 + (-32x5 + 8x7)) = 0 Combine like terms: -32x5 + -32x5 = -64x5 (128x3 + -64x5 + 8x7) = 0 Solving 128x3 + -64x5 + 8x7 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8x3'. 8x3(16 + -8x2 + x4) = 0 Factor a trinomial. 8x3((4 + -1x2)(4 + -1x2)) = 0 Factor a difference between two squares. 8x3(((2 + x)(2 + -1x))(4 + -1x2)) = 0 Factor a difference between two squares. 8x3(((2 + x)(2 + -1x))(2 + x)(2 + -1x)) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 3
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 4
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 5
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 = 2Solution
x = {-2, 2, -2, 2}
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