x^2+2y^2=3

Solution for x^2+2y^2=3 equation:

Simplifying
x2 + 2y2 = 3

Solving
x2 + 2y2 = 3

Solving for variable 'x'.

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

Add '-2y2' to each side of the equation.
x2 + 2y2 + -2y2 = 3 + -2y2

Combine like terms: 2y2 + -2y2 = 0
x2 + 0 = 3 + -2y2
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 + -2y)(x + -1y) = 0

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

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

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

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

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