2u^2+2v^2+4=0

Solution for 2u^2+2v^2+4=0 equation:

Simplifying
2u2 + 2v2 + 4 = 0

Reorder the terms:
4 + 2u2 + 2v2 = 0

Solving
4 + 2u2 + 2v2 = 0

Solving for variable 'u'.

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

Add '-4' to each side of the equation.
4 + 2u2 + -4 + 2v2 = 0 + -4

Reorder the terms:
4 + -4 + 2u2 + 2v2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 2u2 + 2v2 = 0 + -4
2u2 + 2v2 = 0 + -4

Combine like terms: 0 + -4 = -4
2u2 + 2v2 = -4

Add '-2v2' to each side of the equation.
2u2 + 2v2 + -2v2 = -4 + -2v2

Combine like terms: 2v2 + -2v2 = 0
2u2 + 0 = -4 + -2v2
2u2 = -4 + -2v2

Divide each side by '2'.
u2 = -2 + -1v2

Simplifying
u2 = -2 + -1v2

Reorder the terms:
2 + u2 + v2 = -2 + -1v2 + 2 + v2

Reorder the terms:
2 + u2 + v2 = -2 + 2 + -1v2 + v2

Combine like terms: -2 + 2 = 0
2 + u2 + v2 = 0 + -1v2 + v2
2 + u2 + v2 = -1v2 + v2

Combine like terms: -1v2 + v2 = 0
2 + u2 + v2 = 0

Factor a trinomial.
(u + v)(u + v) = 0

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

Simplifying
u + v = 0

Solving
u + v = 0

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

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

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

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

Simplifying
u + v = 0

Solving
u + v = 0

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

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

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

Simplifying
u = -1v
Solution
u = {-1v, -1v}