V^2-5=-8-2v^2

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Solution for V^2-5=-8-2v^2 equation: 


Simplifying
V2 + -5 = -8 + -2v2

Reorder the terms:
-5 + V2 = -8 + -2v2

Solving
-5 + V2 = -8 + -2v2

Solving for variable 'V'.

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

Add '5' to each side of the equation.
-5 + 5 + V2 = -8 + 5 + -2v2

Combine like terms: -5 + 5 = 0
0 + V2 = -8 + 5 + -2v2
V2 = -8 + 5 + -2v2

Combine like terms: -8 + 5 = -3
V2 = -3 + -2v2

Simplifying
V2 = -3 + -2v2

Reorder the terms:
3 + V2 + 2v2 = -3 + -2v2 + 3 + 2v2

Reorder the terms:
3 + V2 + 2v2 = -3 + 3 + -2v2 + 2v2

Combine like terms: -3 + 3 = 0
3 + V2 + 2v2 = 0 + -2v2 + 2v2
3 + V2 + 2v2 = -2v2 + 2v2

Combine like terms: -2v2 + 2v2 = 0
3 + V2 + 2v2 = 0

Factor a trinomial.
(V + v)(V + 2v) = 0


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

Simplifying
V + v = 0

Solving
V + v = 0

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

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

Combine like terms: v + -1v = 0
V + 0 = 0 + -1v
V = 0 + -1v
Remove the zero:
V = -1v

Simplifying
V = -1v

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

Simplifying
V + 2v = 0

Solving
V + 2v = 0

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

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

Combine like terms: 2v + -2v = 0
V + 0 = 0 + -2v
V = 0 + -2v
Remove the zero:
V = -2v

Simplifying
V = -2v
Solution
V = {-1v, -2v}

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