v^2-2v=40+v

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Solution for v^2-2v=40+v equation: 


Simplifying
v2 + -2v = 40 + v

Reorder the terms:
-2v + v2 = 40 + v

Solving
-2v + v2 = 40 + v

Solving for variable 'v'.

Reorder the terms:
-40 + -2v + -1v + v2 = 40 + v + -40 + -1v

Combine like terms: -2v + -1v = -3v
-40 + -3v + v2 = 40 + v + -40 + -1v

Reorder the terms:
-40 + -3v + v2 = 40 + -40 + v + -1v

Combine like terms: 40 + -40 = 0
-40 + -3v + v2 = 0 + v + -1v
-40 + -3v + v2 = v + -1v

Combine like terms: v + -1v = 0
-40 + -3v + v2 = 0

Factor a trinomial.
(-5 + -1v)(8 + -1v) = 0


Subproblem 1
Set the factor '(-5 + -1v)' equal to zero and attempt to solve:

Simplifying
-5 + -1v = 0

Solving
-5 + -1v = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1v = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1v = 0 + 5
-1v = 0 + 5

Combine like terms: 0 + 5 = 5
-1v = 5

Divide each side by '-1'.
v = -5

Simplifying
v = -5

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 = {-5, 8}

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