4((x^3)-(9x))=0

Solution for 4((x^3)-(9x))=0 equation:

Simplifying
4((x3) + -1(9x)) = 0
4(x3 + -1(9x)) = 0

Remove parenthesis around (9x)
4(x3 + -1 * 9x) = 0

Multiply -1 * 9
4(x3 + -9x) = 0

Reorder the terms:
4(-9x + x3) = 0
(-9x * 4 + x3 * 4) = 0
(-36x + 4x3) = 0

Solving
-36x + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-9 + x2) = 0

Factor a difference between two squares.
4x((3 + x)(-3 + 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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

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

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

Add '3' to each side of the equation.
-3 + 3 + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Simplifying
x = 3
Solution
x = {0, -3, 3}