8x^3=x

Solution for 8x^3=x equation:

Simplifying
8x3 = x

Solving
8x3 = x

Solving for variable 'x'.

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

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

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

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 + 8x2)' equal to zero and attempt to solve:

Simplifying
-1 + 8x2 = 0

Solving
-1 + 8x2 = 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 + 8x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 8x2 = 0 + 1
8x2 = 0 + 1

Combine like terms: 0 + 1 = 1
8x2 = 1

Divide each side by '8'.
x2 = 0.125

Simplifying
x2 = 0.125

Take the square root of each side:
x = {-0.353553391, 0.353553391}
Solution
x = {0, -0.353553391, 0.353553391}