0=-x(x^2-4)

Solution for 0=-x(x^2-4) equation:

Simplifying
0 = -1x(x2 + -4)

Reorder the terms:
0 = -1x(-4 + x2)
0 = (-4 * -1x + x2 * -1x)
0 = (4x + -1x3)

Solving
0 = 4x + -1x3

Solving for variable 'x'.
Remove the zero:
-4x + x3 = 4x + -1x3 + -4x + x3

Reorder the terms:
-4x + x3 = 4x + -4x + -1x3 + x3

Combine like terms: 4x + -4x = 0
-4x + x3 = 0 + -1x3 + x3
-4x + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
-4x + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-4 + x2) = 0

Factor a difference between two squares.
x((2 + x)(-2 + x)) = 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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Subproblem 3
Set the factor '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

Solving
-2 + x = 0

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

Add '2' to each side of the equation.
-2 + 2 + x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x = 0 + 2
x = 0 + 2

Combine like terms: 0 + 2 = 2
x = 2

Simplifying
x = 2
Solution
x = {0, -2, 2}