x(x*3)(x^2-16)=0

Solution for x(x*3)(x^2-16)=0 equation:

Simplifying
x(x * 3)(x2 + -16) = 0

Reorder the terms for easier multiplication:
x(3x)(x2 + -16) = 0

Remove parenthesis around (3x)
x * 3x(x2 + -16) = 0

Reorder the terms:
x * 3x(-16 + x2) = 0

Reorder the terms for easier multiplication:
3x * x(-16 + x2) = 0

Multiply x * x
3x2(-16 + x2) = 0
(-16 * 3x2 + x2 * 3x2) = 0
(-48x2 + 3x4) = 0

Solving
-48x2 + 3x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x2'.
3x2(-16 + x2) = 0

Factor a difference between two squares.
3x2((4 + x)(-4 + x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
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}