z^6-1=

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Solution for z^6-1= 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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