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

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

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

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

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

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

Combine like terms: 6x + 6x = 12x
(18 + 12x + 2x2) = 0

Solving
18 + 12x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 6x + x2) = 0

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

Ignore the factor 2.
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 '(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 = {-3, -3}