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

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

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

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

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

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

Combine like terms: 6x + 9x = 15x
(18 + 15x + 3x2) = 0

Solving
18 + 15x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + 5x + x2) = 0

Factor a trinomial.
3((3 + x)(2 + x)) = 0

Ignore the factor 3.
Subproblem 1
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 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 = {-3, -2}