x^3-13x=0

Solution for x^3-13x=0 equation:

Simplifying
x3 + -13x = 0

Reorder the terms:
-13x + x3 = 0

Solving
-13x + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-13 + x2) = 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 '(-13 + x2)' equal to zero and attempt to solve:

Simplifying
-13 + x2 = 0

Solving
-13 + x2 = 0

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

Add '13' to each side of the equation.
-13 + 13 + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + x2 = 0 + 13
x2 = 0 + 13

Combine like terms: 0 + 13 = 13
x2 = 13

Simplifying
x2 = 13

Take the square root of each side:
x = {-3.605551275, 3.605551275}
Solution
x = {0, -3.605551275, 3.605551275}