b(b+9)=4(5+2b)

Solution for b(b+9)=4(5+2b) equation:

Simplifying
b(b + 9) = 4(5 + 2b)

Reorder the terms:
b(9 + b) = 4(5 + 2b)
(9 * b + b * b) = 4(5 + 2b)
(9b + b2) = 4(5 + 2b)
9b + b2 = (5 * 4 + 2b * 4)
9b + b2 = (20 + 8b)

Solving
9b + b2 = 20 + 8b

Solving for variable 'b'.

Reorder the terms:
-20 + 9b + -8b + b2 = 20 + 8b + -20 + -8b

Combine like terms: 9b + -8b = 1b
-20 + 1b + b2 = 20 + 8b + -20 + -8b

Reorder the terms:
-20 + 1b + b2 = 20 + -20 + 8b + -8b

Combine like terms: 20 + -20 = 0
-20 + 1b + b2 = 0 + 8b + -8b
-20 + 1b + b2 = 8b + -8b

Combine like terms: 8b + -8b = 0
-20 + 1b + b2 = 0

Factor a trinomial.
(-5 + -1b)(4 + -1b) = 0

Subproblem 1
Set the factor '(-5 + -1b)' equal to zero and attempt to solve:

Simplifying
-5 + -1b = 0

Solving
-5 + -1b = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1b = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1b = 0 + 5
-1b = 0 + 5

Combine like terms: 0 + 5 = 5
-1b = 5

Divide each side by '-1'.
b = -5

Simplifying
b = -5
Subproblem 2
Set the factor '(4 + -1b)' equal to zero and attempt to solve:

Simplifying
4 + -1b = 0

Solving
4 + -1b = 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 + -1b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1b = 0 + -4
-1b = 0 + -4

Combine like terms: 0 + -4 = -4
-1b = -4

Divide each side by '-1'.
b = 4

Simplifying
b = 4
Solution
b = {-5, 4}