(3b+5)(b+3)=7

Solution for (3b+5)(b+3)=7 equation:

Simplifying
(3b + 5)(b + 3) = 7

Reorder the terms:
(5 + 3b)(b + 3) = 7

Reorder the terms:
(5 + 3b)(3 + b) = 7

Multiply (5 + 3b) * (3 + b)
(5(3 + b) + 3b * (3 + b)) = 7
((3 * 5 + b * 5) + 3b * (3 + b)) = 7
((15 + 5b) + 3b * (3 + b)) = 7
(15 + 5b + (3 * 3b + b * 3b)) = 7
(15 + 5b + (9b + 3b2)) = 7

Combine like terms: 5b + 9b = 14b
(15 + 14b + 3b2) = 7

Solving
15 + 14b + 3b2 = 7

Solving for variable 'b'.

Reorder the terms:
15 + -7 + 14b + 3b2 = 7 + -7

Combine like terms: 15 + -7 = 8
8 + 14b + 3b2 = 7 + -7

Combine like terms: 7 + -7 = 0
8 + 14b + 3b2 = 0

Factor a trinomial.
(4 + b)(2 + 3b) = 0

Subproblem 1
Set the factor '(4 + b)' equal to zero and attempt to solve:

Simplifying
4 + b = 0

Solving
4 + b = 0

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

Add '-4' to each side of the equation.
4 + -4 + b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + b = 0 + -4
b = 0 + -4

Combine like terms: 0 + -4 = -4
b = -4

Simplifying
b = -4
Subproblem 2
Set the factor '(2 + 3b)' equal to zero and attempt to solve:

Simplifying
2 + 3b = 0

Solving
2 + 3b = 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 + 3b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3b = 0 + -2
3b = 0 + -2

Combine like terms: 0 + -2 = -2
3b = -2

Divide each side by '3'.
b = -0.6666666667

Simplifying
b = -0.6666666667
Solution
b = {-4, -0.6666666667}