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

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

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

Reorder the terms:
(3 + 2b)(b + 3) = 0

Reorder the terms:
(3 + 2b)(3 + b) = 0

Multiply (3 + 2b) * (3 + b)
(3(3 + b) + 2b * (3 + b)) = 0
((3 * 3 + b * 3) + 2b * (3 + b)) = 0
((9 + 3b) + 2b * (3 + b)) = 0
(9 + 3b + (3 * 2b + b * 2b)) = 0
(9 + 3b + (6b + 2b2)) = 0

Combine like terms: 3b + 6b = 9b
(9 + 9b + 2b2) = 0

Solving
9 + 9b + 2b2 = 0

Solving for variable 'b'.

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

Subproblem 1
Set the factor '(3 + b)' equal to zero and attempt to solve:

Simplifying
3 + b = 0

Solving
3 + b = 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 + b = 0 + -3

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

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

Simplifying
b = -3
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 = {-3, -1.5}