8x-1=8x^3-1

Solution for 8x-1=8x^3-1 equation:

Simplifying
8x + -1 = 8x3 + -1

Reorder the terms:
-1 + 8x = 8x3 + -1

Reorder the terms:
-1 + 8x = -1 + 8x3

Add '1' to each side of the equation.
-1 + 1 + 8x = -1 + 1 + 8x3

Combine like terms: -1 + 1 = 0
0 + 8x = -1 + 1 + 8x3
8x = -1 + 1 + 8x3

Combine like terms: -1 + 1 = 0
8x = 0 + 8x3
8x = 8x3

Solving
8x = 8x3

Solving for variable 'x'.

Combine like terms: 8x3 + -8x3 = 0
8x + -8x3 = 0

Factor out the Greatest Common Factor (GCF), '8x'.
8x(1 + -1x2) = 0

Factor a difference between two squares.
8x((1 + x)(1 + -1x)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0, -1, 1}