(x^106)-1=0

Solution for (x^106)-1=0 equation:

Simplifying
(x106) + -1 = 0
x106 + -1 = 0

Reorder the terms:
-1 + x106 = 0

Solving
-1 + x106 = 0

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x106 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + x106 = 0 + 1
x106 = 0 + 1

Combine like terms: 0 + 1 = 1
x106 = 1

Simplifying
x106 = 1

Reorder the terms:
-1 + x106 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + x106 = 0

Factor a difference between two squares.
(1 + x53)(-1 + x53) = 0

Subproblem 1
Set the factor '(1 + x53)' equal to zero and attempt to solve:

Simplifying
1 + x53 = 0

Solving
1 + x53 = 0

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

Add '-1' to each side of the equation.
1 + -1 + x53 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x53 = 0 + -1
x53 = 0 + -1

Combine like terms: 0 + -1 = -1
x53 = -1

Simplifying
x53 = -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 + x53)' equal to zero and attempt to solve:

Simplifying
-1 + x53 = 0

Solving
-1 + x53 = 0

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

Add '1' to each side of the equation.
-1 + 1 + x53 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + x53 = 0 + 1
x53 = 0 + 1

Combine like terms: 0 + 1 = 1
x53 = 1

Simplifying
x53 = 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.