b^2-4b=2b+16

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Solution for b^2-4b=2b+16 equation: 


Simplifying
b2 + -4b = 2b + 16

Reorder the terms:
-4b + b2 = 2b + 16

Reorder the terms:
-4b + b2 = 16 + 2b

Solving
-4b + b2 = 16 + 2b

Solving for variable 'b'.

Reorder the terms:
-16 + -4b + -2b + b2 = 16 + 2b + -16 + -2b

Combine like terms: -4b + -2b = -6b
-16 + -6b + b2 = 16 + 2b + -16 + -2b

Reorder the terms:
-16 + -6b + b2 = 16 + -16 + 2b + -2b

Combine like terms: 16 + -16 = 0
-16 + -6b + b2 = 0 + 2b + -2b
-16 + -6b + b2 = 2b + -2b

Combine like terms: 2b + -2b = 0
-16 + -6b + b2 = 0

Factor a trinomial.
(-2 + -1b)(8 + -1b) = 0


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

Simplifying
-2 + -1b = 0

Solving
-2 + -1b = 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 + -1b = 0 + 2

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

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

Divide each side by '-1'.
b = -2

Simplifying
b = -2

Subproblem 2
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
Solution
b = {-2, 8}

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