3(x+2)*(3x+6)=0

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

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

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

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

Multiply (2 + x) * (6 + 3x)
3(2(6 + 3x) + x(6 + 3x)) = 0
3((6 * 2 + 3x * 2) + x(6 + 3x)) = 0
3((12 + 6x) + x(6 + 3x)) = 0
3(12 + 6x + (6 * x + 3x * x)) = 0
3(12 + 6x + (6x + 3x2)) = 0

Combine like terms: 6x + 6x = 12x
3(12 + 12x + 3x2) = 0
(12 * 3 + 12x * 3 + 3x2 * 3) = 0
(36 + 36x + 9x2) = 0

Solving
36 + 36x + 9x2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
9((2 + x)(2 + x)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-2, -2}