b(b+20)=6(8+3b)

Solution for b(b+20)=6(8+3b) equation:

Simplifying
b(b + 20) = 6(8 + 3b)

Reorder the terms:
b(20 + b) = 6(8 + 3b)
(20 * b + b * b) = 6(8 + 3b)
(20b + b2) = 6(8 + 3b)
20b + b2 = (8 * 6 + 3b * 6)
20b + b2 = (48 + 18b)

Solving
20b + b2 = 48 + 18b

Solving for variable 'b'.

Reorder the terms:
-48 + 20b + -18b + b2 = 48 + 18b + -48 + -18b

Combine like terms: 20b + -18b = 2b
-48 + 2b + b2 = 48 + 18b + -48 + -18b

Reorder the terms:
-48 + 2b + b2 = 48 + -48 + 18b + -18b

Combine like terms: 48 + -48 = 0
-48 + 2b + b2 = 0 + 18b + -18b
-48 + 2b + b2 = 18b + -18b

Combine like terms: 18b + -18b = 0
-48 + 2b + b2 = 0

Factor a trinomial.
(-8 + -1b)(6 + -1b) = 0

Subproblem 1
Set the factor '(-8 + -1b)' equal to zero and attempt to solve:

Simplifying
-8 + -1b = 0

Solving
-8 + -1b = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1b = 0 + 8

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

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

Divide each side by '-1'.
b = -8

Simplifying
b = -8
Subproblem 2
Set the factor '(6 + -1b)' equal to zero and attempt to solve:

Simplifying
6 + -1b = 0

Solving
6 + -1b = 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 + -1b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1b = 0 + -6
-1b = 0 + -6

Combine like terms: 0 + -6 = -6
-1b = -6

Divide each side by '-1'.
b = 6

Simplifying
b = 6
Solution
b = {-8, 6}