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

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

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

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

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

Multiply (6 + 3x) * (3 + 2x)
(6(3 + 2x) + 3x * (3 + 2x)) = 0
((3 * 6 + 2x * 6) + 3x * (3 + 2x)) = 0
((18 + 12x) + 3x * (3 + 2x)) = 0
(18 + 12x + (3 * 3x + 2x * 3x)) = 0
(18 + 12x + (9x + 6x2)) = 0

Combine like terms: 12x + 9x = 21x
(18 + 21x + 6x2) = 0

Solving
18 + 21x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + 7x + 2x2) = 0

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

Ignore the factor 3.
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 '(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 = {-2, -1.5}