0=(x^3)-9x

Solution for 0=(x^3)-9x equation:

Simplifying
0 = (x3) + -9x
0 = x3 + -9x

Reorder the terms:
0 = -9x + x3

Solving
0 = -9x + x3

Solving for variable 'x'.
Remove the zero:
9x + -1x3 = -9x + x3 + 9x + -1x3

Reorder the terms:
9x + -1x3 = -9x + 9x + x3 + -1x3

Combine like terms: -9x + 9x = 0
9x + -1x3 = 0 + x3 + -1x3
9x + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
9x + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(9 + -1x2) = 0

Factor a difference between two squares.
x((3 + x)(3 + -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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, -3, 3}