v^2-4v=16+2v

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


Simplifying
v2 + -4v = 16 + 2v

Reorder the terms:
-4v + v2 = 16 + 2v

Solving
-4v + v2 = 16 + 2v

Solving for variable 'v'.

Reorder the terms:
-16 + -4v + -2v + v2 = 16 + 2v + -16 + -2v

Combine like terms: -4v + -2v = -6v
-16 + -6v + v2 = 16 + 2v + -16 + -2v

Reorder the terms:
-16 + -6v + v2 = 16 + -16 + 2v + -2v

Combine like terms: 16 + -16 = 0
-16 + -6v + v2 = 0 + 2v + -2v
-16 + -6v + v2 = 2v + -2v

Combine like terms: 2v + -2v = 0
-16 + -6v + v2 = 0

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


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

Simplifying
-2 + -1v = 0

Solving
-2 + -1v = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1v = 0 + 2

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

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

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

Simplifying
v = -2

Subproblem 2
Set the factor '(8 + -1v)' equal to zero and attempt to solve:

Simplifying
8 + -1v = 0

Solving
8 + -1v = 0

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

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

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

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

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

Simplifying
v = 8
Solution
v = {-2, 8}

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