(8b+3)(6b+7)=0

Solution for (8b+3)(6b+7)=0 equation:

Simplifying
(8b + 3)(6b + 7) = 0

Reorder the terms:
(3 + 8b)(6b + 7) = 0

Reorder the terms:
(3 + 8b)(7 + 6b) = 0

Multiply (3 + 8b) * (7 + 6b)
(3(7 + 6b) + 8b * (7 + 6b)) = 0
((7 * 3 + 6b * 3) + 8b * (7 + 6b)) = 0
((21 + 18b) + 8b * (7 + 6b)) = 0
(21 + 18b + (7 * 8b + 6b * 8b)) = 0
(21 + 18b + (56b + 48b2)) = 0

Combine like terms: 18b + 56b = 74b
(21 + 74b + 48b2) = 0

Solving
21 + 74b + 48b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(7 + 6b)(3 + 8b) = 0

Subproblem 1
Set the factor '(7 + 6b)' equal to zero and attempt to solve:

Simplifying
7 + 6b = 0

Solving
7 + 6b = 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 + 6b = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 6b = 0 + -7
6b = 0 + -7

Combine like terms: 0 + -7 = -7
6b = -7

Divide each side by '6'.
b = -1.166666667

Simplifying
b = -1.166666667
Subproblem 2
Set the factor '(3 + 8b)' equal to zero and attempt to solve:

Simplifying
3 + 8b = 0

Solving
3 + 8b = 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 + 8b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8b = 0 + -3
8b = 0 + -3

Combine like terms: 0 + -3 = -3
8b = -3

Divide each side by '8'.
b = -0.375

Simplifying
b = -0.375
Solution
b = {-1.166666667, -0.375}