(5b+7)(b+5)=23

Solution for (5b+7)(b+5)=23 equation:

Simplifying
(5b + 7)(b + 5) = 23

Reorder the terms:
(7 + 5b)(b + 5) = 23

Reorder the terms:
(7 + 5b)(5 + b) = 23

Multiply (7 + 5b) * (5 + b)
(7(5 + b) + 5b * (5 + b)) = 23
((5 * 7 + b * 7) + 5b * (5 + b)) = 23
((35 + 7b) + 5b * (5 + b)) = 23
(35 + 7b + (5 * 5b + b * 5b)) = 23
(35 + 7b + (25b + 5b2)) = 23

Combine like terms: 7b + 25b = 32b
(35 + 32b + 5b2) = 23

Solving
35 + 32b + 5b2 = 23

Solving for variable 'b'.

Reorder the terms:
35 + -23 + 32b + 5b2 = 23 + -23

Combine like terms: 35 + -23 = 12
12 + 32b + 5b2 = 23 + -23

Combine like terms: 23 + -23 = 0
12 + 32b + 5b2 = 0

Factor a trinomial.
(6 + b)(2 + 5b) = 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 '(2 + 5b)' equal to zero and attempt to solve:

Simplifying
2 + 5b = 0

Solving
2 + 5b = 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 + 5b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5b = 0 + -2
5b = 0 + -2

Combine like terms: 0 + -2 = -2
5b = -2

Divide each side by '5'.
b = -0.4

Simplifying
b = -0.4
Solution
b = {-6, -0.4}