0=-4x^3+64x

Solution for 0=-4x^3+64x equation:

Simplifying
0 = -4x3 + 64x

Reorder the terms:
0 = 64x + -4x3

Solving
0 = 64x + -4x3

Solving for variable 'x'.
Remove the zero:
-64x + 4x3 = 64x + -4x3 + -64x + 4x3

Reorder the terms:
-64x + 4x3 = 64x + -64x + -4x3 + 4x3

Combine like terms: 64x + -64x = 0
-64x + 4x3 = 0 + -4x3 + 4x3
-64x + 4x3 = -4x3 + 4x3

Combine like terms: -4x3 + 4x3 = 0
-64x + 4x3 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-16 + x2) = 0

Factor a difference between two squares.
4x((4 + x)(-4 + x)) = 0

Ignore the factor 4.
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 + 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
Solution
x = {0, -4, 4}