5x^3-x=0

Solution for 5x^3-x=0 equation:

Simplifying
5x3 + -1x = 0

Reorder the terms:
-1x + 5x3 = 0

Solving
-1x + 5x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + 5x2) = 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 + 5x2)' equal to zero and attempt to solve:

Simplifying
-1 + 5x2 = 0

Solving
-1 + 5x2 = 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 + 5x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 5x2 = 0 + 1
5x2 = 0 + 1

Combine like terms: 0 + 1 = 1
5x2 = 1

Divide each side by '5'.
x2 = 0.2

Simplifying
x2 = 0.2

Take the square root of each side:
x = {-0.447213596, 0.447213596}
Solution
x = {0, -0.447213596, 0.447213596}