0=x^2+3xy+2y^2

Solution for 0=x^2+3xy+2y^2 equation:

Simplifying
0 = x2 + 3xy + 2y2

Reorder the terms:
0 = 3xy + x2 + 2y2

Solving
0 = 3xy + x2 + 2y2

Solving for variable 'x'.
Remove the zero:
-3xy + -1x2 + -2y2 = 3xy + x2 + 2y2 + -3xy + -1x2 + -2y2

Reorder the terms:
-3xy + -1x2 + -2y2 = 3xy + -3xy + x2 + -1x2 + 2y2 + -2y2

Combine like terms: 3xy + -3xy = 0
-3xy + -1x2 + -2y2 = 0 + x2 + -1x2 + 2y2 + -2y2
-3xy + -1x2 + -2y2 = x2 + -1x2 + 2y2 + -2y2

Combine like terms: x2 + -1x2 = 0
-3xy + -1x2 + -2y2 = 0 + 2y2 + -2y2
-3xy + -1x2 + -2y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-3xy + -1x2 + -2y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3xy + x2 + 2y2) = 0

Factor a trinomial.
-1((x + y)(x + 2y)) = 0

Ignore the factor -1.
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}