Z^6-1=0

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Solution for Z^6-1=0 equation:


Simplifying
Z6 + -1 = 0

Reorder the terms:
-1 + Z6 = 0

Solving
-1 + Z6 = 0

Solving for variable 'Z'.

Move all terms containing Z to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + Z6 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + Z6 = 0 + 1
Z6 = 0 + 1

Combine like terms: 0 + 1 = 1
Z6 = 1

Simplifying
Z6 = 1

Reorder the terms:
-1 + Z6 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + Z6 = 0

Factor a difference between two squares.
(1 + Z3)(-1 + Z3) = 0

Subproblem 1

Set the factor '(1 + Z3)' equal to zero and attempt to solve: Simplifying 1 + Z3 = 0 Solving 1 + Z3 = 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 + Z3 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + Z3 = 0 + -1 Z3 = 0 + -1 Combine like terms: 0 + -1 = -1 Z3 = -1 Simplifying Z3 = -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 + Z3)' equal to zero and attempt to solve: Simplifying -1 + Z3 = 0 Solving -1 + Z3 = 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 + Z3 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + Z3 = 0 + 1 Z3 = 0 + 1 Combine like terms: 0 + 1 = 1 Z3 = 1 Simplifying Z3 = 1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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