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Simplifying (z8) + -1(2z4) + 1 = 0 z8 + -1(2z4) + 1 = 0 Remove parenthesis around (2z4) z8 + -1 * 2z4 + 1 = 0 Multiply -1 * 2 z8 + -2z4 + 1 = 0 Reorder the terms: 1 + -2z4 + z8 = 0 Solving 1 + -2z4 + z8 = 0 Solving for variable 'z'. Factor a trinomial. (1 + -1z4)(1 + -1z4) = 0 Factor a difference between two squares. ((1 + z2)(1 + -1z2))(1 + -1z4) = 0 Factor a difference between two squares. ((1 + z2)((1 + z)(1 + -1z)))(1 + -1z4) = 0 Factor a difference between two squares. ((1 + z2)(1 + -1z2))(1 + z2)(1 + z)(1 + -1z) = 0 Factor a difference between two squares. ((1 + z2)((1 + z)(1 + -1z)))(1 + z2)(1 + z)(1 + -1z) = 0Subproblem 1
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 2
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 3
Set the factor '(1 + -1z)' equal to zero and attempt to solve: Simplifying 1 + -1z = 0 Solving 1 + -1z = 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 + -1z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1z = 0 + -1 -1z = 0 + -1 Combine like terms: 0 + -1 = -1 -1z = -1 Divide each side by '-1'. z = 1 Simplifying z = 1Subproblem 4
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 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 = -1Subproblem 6
Set the factor '(1 + -1z)' equal to zero and attempt to solve: Simplifying 1 + -1z = 0 Solving 1 + -1z = 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 + -1z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1z = 0 + -1 -1z = 0 + -1 Combine like terms: 0 + -1 = -1 -1z = -1 Divide each side by '-1'. z = 1 Simplifying z = 1Solution
z = {-1, 1, -1, 1}
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