(2b+1)(b+3)=0

Solution for (2b+1)(b+3)=0 equation:

Simplifying
(2b + 1)(b + 3) = 0

Reorder the terms:
(1 + 2b)(b + 3) = 0

Reorder the terms:
(1 + 2b)(3 + b) = 0

Multiply (1 + 2b) * (3 + b)
(1(3 + b) + 2b * (3 + b)) = 0
((3 * 1 + b * 1) + 2b * (3 + b)) = 0
((3 + 1b) + 2b * (3 + b)) = 0
(3 + 1b + (3 * 2b + b * 2b)) = 0
(3 + 1b + (6b + 2b2)) = 0

Combine like terms: 1b + 6b = 7b
(3 + 7b + 2b2) = 0

Solving
3 + 7b + 2b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(3 + b)(1 + 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 '(1 + 2b)' equal to zero and attempt to solve:

Simplifying
1 + 2b = 0

Solving
1 + 2b = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2b = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2b = 0 + -1
2b = 0 + -1

Combine like terms: 0 + -1 = -1
2b = -1

Divide each side by '2'.
b = -0.5

Simplifying
b = -0.5
Solution
b = {-3, -0.5}