0=x^3-36x

Solution for 0=x^3-36x equation:

Simplifying
0 = x3 + -36x

Reorder the terms:
0 = -36x + x3

Solving
0 = -36x + x3

Solving for variable 'x'.
Remove the zero:
36x + -1x3 = -36x + x3 + 36x + -1x3

Reorder the terms:
36x + -1x3 = -36x + 36x + x3 + -1x3

Combine like terms: -36x + 36x = 0
36x + -1x3 = 0 + x3 + -1x3
36x + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
36x + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(36 + -1x2) = 0

Factor a difference between two squares.
x((6 + x)(6 + -1x)) = 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 '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0, -6, 6}