0=x^3-16x

Solution for 0=x^3-16x equation:

Simplifying
0 = x3 + -16x

Reorder the terms:
0 = -16x + x3

Solving
0 = -16x + x3

Solving for variable 'x'.
Remove the zero:
16x + -1x3 = -16x + x3 + 16x + -1x3

Reorder the terms:
16x + -1x3 = -16x + 16x + x3 + -1x3

Combine like terms: -16x + 16x = 0
16x + -1x3 = 0 + x3 + -1x3
16x + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
16x + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(16 + -1x2) = 0

Factor a difference between two squares.
x((4 + x)(4 + -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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0, -4, 4}