0=4x(x^2-36)

Solution for 0=4x(x^2-36) equation:

Simplifying
0 = 4x(x2 + -36)

Reorder the terms:
0 = 4x(-36 + x2)
0 = (-36 * 4x + x2 * 4x)
0 = (-144x + 4x3)

Solving
0 = -144x + 4x3

Solving for variable 'x'.
Remove the zero:
144x + -4x3 = -144x + 4x3 + 144x + -4x3

Reorder the terms:
144x + -4x3 = -144x + 144x + 4x3 + -4x3

Combine like terms: -144x + 144x = 0
144x + -4x3 = 0 + 4x3 + -4x3
144x + -4x3 = 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
144x + -4x3 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(36 + -1x2) = 0

Factor a difference between two squares.
4x((6 + x)(6 + -1x)) = 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 '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0, -6, 6}