b(b+24)=5(4+5b)

Solution for b(b+24)=5(4+5b) equation:

Simplifying
b(b + 24) = 5(4 + 5b)

Reorder the terms:
b(24 + b) = 5(4 + 5b)
(24 * b + b * b) = 5(4 + 5b)
(24b + b2) = 5(4 + 5b)
24b + b2 = (4 * 5 + 5b * 5)
24b + b2 = (20 + 25b)

Solving
24b + b2 = 20 + 25b

Solving for variable 'b'.

Reorder the terms:
-20 + 24b + -25b + b2 = 20 + 25b + -20 + -25b

Combine like terms: 24b + -25b = -1b
-20 + -1b + b2 = 20 + 25b + -20 + -25b

Reorder the terms:
-20 + -1b + b2 = 20 + -20 + 25b + -25b

Combine like terms: 20 + -20 = 0
-20 + -1b + b2 = 0 + 25b + -25b
-20 + -1b + b2 = 25b + -25b

Combine like terms: 25b + -25b = 0
-20 + -1b + b2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
b = {-4, 5}