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

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

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

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

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

Multiply (3 + 2x) * (6 + 2x)
(3(6 + 2x) + 2x * (6 + 2x)) = 0
((6 * 3 + 2x * 3) + 2x * (6 + 2x)) = 0
((18 + 6x) + 2x * (6 + 2x)) = 0
(18 + 6x + (6 * 2x + 2x * 2x)) = 0
(18 + 6x + (12x + 4x2)) = 0

Combine like terms: 6x + 12x = 18x
(18 + 18x + 4x2) = 0

Solving
18 + 18x + 4x2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
2((3 + x)(3 + 2x)) = 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 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {-3, -1.5}