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Simplifying z9 + -1z = 0 Reorder the terms: -1z + z9 = 0 Solving -1z + z9 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-1 + z8) = 0 Factor a difference between two squares. z((1 + z4)(-1 + z4)) = 0 Factor a difference between two squares. z((1 + z4)((1 + z2)(-1 + z2))) = 0 Factor a difference between two squares. z((1 + z4)((1 + z2)((1 + z)(-1 + z)))) = 0Subproblem 1
Set the factor 'z' equal to zero and attempt to solve: Simplifying z = 0 Solving z = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z = 0Subproblem 2
Set the factor '(1 + z4)' equal to zero and attempt to solve: Simplifying 1 + z4 = 0 Solving 1 + z4 = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + z4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + z4 = 0 + -1 z4 = 0 + -1 Combine like terms: 0 + -1 = -1 z4 = -1 Simplifying z4 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(1 + z2)' equal to zero and attempt to solve: Simplifying 1 + z2 = 0 Solving 1 + z2 = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + z2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + z2 = 0 + -1 z2 = 0 + -1 Combine like terms: 0 + -1 = -1 z2 = -1 Simplifying z2 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 4
Set the factor '(1 + z)' equal to zero and attempt to solve: Simplifying 1 + z = 0 Solving 1 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + z = 0 + -1 z = 0 + -1 Combine like terms: 0 + -1 = -1 z = -1 Simplifying z = -1Subproblem 5
Set the factor '(-1 + z)' equal to zero and attempt to solve: Simplifying -1 + z = 0 Solving -1 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + z = 0 + 1 z = 0 + 1 Combine like terms: 0 + 1 = 1 z = 1 Simplifying z = 1Solution
z = {0, -1, 1}
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