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

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

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

Reorder the terms:
2b(6 + b) + 3(b + 6) = 0
(6 * 2b + b * 2b) + 3(b + 6) = 0
(12b + 2b2) + 3(b + 6) = 0

Reorder the terms:
12b + 2b2 + 3(6 + b) = 0
12b + 2b2 + (6 * 3 + b * 3) = 0
12b + 2b2 + (18 + 3b) = 0

Reorder the terms:
18 + 12b + 3b + 2b2 = 0

Combine like terms: 12b + 3b = 15b
18 + 15b + 2b2 = 0

Solving
18 + 15b + 2b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(6 + b)(3 + 2b) = 0

Subproblem 1
Set the factor '(6 + b)' equal to zero and attempt to solve:

Simplifying
6 + b = 0

Solving
6 + b = 0

Move all terms containing b to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + b = 0 + -6
b = 0 + -6

Combine like terms: 0 + -6 = -6
b = -6

Simplifying
b = -6
Subproblem 2
Set the factor '(3 + 2b)' equal to zero and attempt to solve:

Simplifying
3 + 2b = 0

Solving
3 + 2b = 0

Move all terms containing b to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + 2b = 0 + -3

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

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

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

Simplifying
b = -1.5
Solution
b = {-6, -1.5}