b(b-3)=20-2b

Solution for b(b-3)=20-2b equation:

Simplifying
b(b + -3) = 20 + -2b

Reorder the terms:
b(-3 + b) = 20 + -2b
(-3 * b + b * b) = 20 + -2b
(-3b + b2) = 20 + -2b

Solving
-3b + b2 = 20 + -2b

Solving for variable 'b'.

Reorder the terms:
-20 + -3b + 2b + b2 = 20 + -2b + -20 + 2b

Combine like terms: -3b + 2b = -1b
-20 + -1b + b2 = 20 + -2b + -20 + 2b

Reorder the terms:
-20 + -1b + b2 = 20 + -20 + -2b + 2b

Combine like terms: 20 + -20 = 0
-20 + -1b + b2 = 0 + -2b + 2b
-20 + -1b + b2 = -2b + 2b

Combine like terms: -2b + 2b = 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}