0=x^3-25x

Solution for 0=x^3-25x equation:

Simplifying
0 = x3 + -25x

Reorder the terms:
0 = -25x + x3

Solving
0 = -25x + x3

Solving for variable 'x'.
Remove the zero:
25x + -1x3 = -25x + x3 + 25x + -1x3

Reorder the terms:
25x + -1x3 = -25x + 25x + x3 + -1x3

Combine like terms: -25x + 25x = 0
25x + -1x3 = 0 + x3 + -1x3
25x + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
25x + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(25 + -1x2) = 0

Factor a difference between two squares.
x((5 + x)(5 + -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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0, -5, 5}