(7b+2)(b+3)=0

Solution for (7b+2)(b+3)=0 equation:

Simplifying
(7b + 2)(b + 3) = 0

Reorder the terms:
(2 + 7b)(b + 3) = 0

Reorder the terms:
(2 + 7b)(3 + b) = 0

Multiply (2 + 7b) * (3 + b)
(2(3 + b) + 7b * (3 + b)) = 0
((3 * 2 + b * 2) + 7b * (3 + b)) = 0
((6 + 2b) + 7b * (3 + b)) = 0
(6 + 2b + (3 * 7b + b * 7b)) = 0
(6 + 2b + (21b + 7b2)) = 0

Combine like terms: 2b + 21b = 23b
(6 + 23b + 7b2) = 0

Solving
6 + 23b + 7b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(3 + b)(2 + 7b) = 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 '(2 + 7b)' equal to zero and attempt to solve:

Simplifying
2 + 7b = 0

Solving
2 + 7b = 0

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

Add '-2' to each side of the equation.
2 + -2 + 7b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7b = 0 + -2
7b = 0 + -2

Combine like terms: 0 + -2 = -2
7b = -2

Divide each side by '7'.
b = -0.2857142857

Simplifying
b = -0.2857142857
Solution
b = {-3, -0.2857142857}