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

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

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

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

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

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

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

Solving
18 + 12x + 2x2 = 2

Solving for variable 'x'.

Reorder the terms:
18 + -2 + 12x + 2x2 = 2 + -2

Combine like terms: 18 + -2 = 16
16 + 12x + 2x2 = 2 + -2

Combine like terms: 2 + -2 = 0
16 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 6x + x2) = 0

Factor a trinomial.
2((4 + x)(2 + x)) = 0

Ignore the factor 2.
Subproblem 1
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 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 = {-4, -2}