x(3x-9)(2x+6)=0

Solution for x(3x-9)(2x+6)=0 equation:

Simplifying
x(3x + -9)(2x + 6) = 0

Reorder the terms:
x(-9 + 3x)(2x + 6) = 0

Reorder the terms:
x(-9 + 3x)(6 + 2x) = 0

Multiply (-9 + 3x) * (6 + 2x)
x(-9(6 + 2x) + 3x * (6 + 2x)) = 0
x((6 * -9 + 2x * -9) + 3x * (6 + 2x)) = 0
x((-54 + -18x) + 3x * (6 + 2x)) = 0
x(-54 + -18x + (6 * 3x + 2x * 3x)) = 0
x(-54 + -18x + (18x + 6x2)) = 0

Combine like terms: -18x + 18x = 0
x(-54 + 0 + 6x2) = 0
x(-54 + 6x2) = 0
(-54 * x + 6x2 * x) = 0
(-54x + 6x3) = 0

Solving
-54x + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x'.
6x(-9 + x2) = 0

Factor a difference between two squares.
6x((3 + x)(-3 + x)) = 0

Ignore the factor 6.
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}