2x^2+4y^2+6=0

Solution for 2x^2+4y^2+6=0 equation:

Simplifying
2x2 + 4y2 + 6 = 0

Reorder the terms:
6 + 2x2 + 4y2 = 0

Solving
6 + 2x2 + 4y2 = 0

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + 2x2 + -6 + 4y2 = 0 + -6

Reorder the terms:
6 + -6 + 2x2 + 4y2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 2x2 + 4y2 = 0 + -6
2x2 + 4y2 = 0 + -6

Combine like terms: 0 + -6 = -6
2x2 + 4y2 = -6

Add '-4y2' to each side of the equation.
2x2 + 4y2 + -4y2 = -6 + -4y2

Combine like terms: 4y2 + -4y2 = 0
2x2 + 0 = -6 + -4y2
2x2 = -6 + -4y2

Divide each side by '2'.
x2 = -3 + -2y2

Simplifying
x2 = -3 + -2y2

Reorder the terms:
3 + x2 + 2y2 = -3 + -2y2 + 3 + 2y2

Reorder the terms:
3 + x2 + 2y2 = -3 + 3 + -2y2 + 2y2

Combine like terms: -3 + 3 = 0
3 + x2 + 2y2 = 0 + -2y2 + 2y2
3 + x2 + 2y2 = -2y2 + 2y2

Combine like terms: -2y2 + 2y2 = 0
3 + x2 + 2y2 = 0

Factor a trinomial.
(x + y)(x + 2y) = 0

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

Simplifying
x + y = 0

Solving
x + y = 0

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

Add '-1y' to each side of the equation.
x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
x + 0 = 0 + -1y
x = 0 + -1y
Remove the zero:
x = -1y

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

Simplifying
x + 2y = 0

Solving
x + 2y = 0

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

Add '-2y' to each side of the equation.
x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
x + 0 = 0 + -2y
x = 0 + -2y
Remove the zero:
x = -2y

Simplifying
x = -2y
Solution
x = {-1y, -2y}