(3b+7)(b+6)=0

Solution for (3b+7)(b+6)=0 equation:

Simplifying
(3b + 7)(b + 6) = 0

Reorder the terms:
(7 + 3b)(b + 6) = 0

Reorder the terms:
(7 + 3b)(6 + b) = 0

Multiply (7 + 3b) * (6 + b)
(7(6 + b) + 3b * (6 + b)) = 0
((6 * 7 + b * 7) + 3b * (6 + b)) = 0
((42 + 7b) + 3b * (6 + b)) = 0
(42 + 7b + (6 * 3b + b * 3b)) = 0
(42 + 7b + (18b + 3b2)) = 0

Combine like terms: 7b + 18b = 25b
(42 + 25b + 3b2) = 0

Solving
42 + 25b + 3b2 = 0

Solving for variable 'b'.

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

Simplifying
7 + 3b = 0

Solving
7 + 3b = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3b = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3b = 0 + -7
3b = 0 + -7

Combine like terms: 0 + -7 = -7
3b = -7

Divide each side by '3'.
b = -2.333333333

Simplifying
b = -2.333333333
Solution
b = {-6, -2.333333333}