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

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

Simplifying
x2 + -2xy + -3y2 = 0

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

Solving
-2xy + x2 + -3y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -3y)(x + y) = 0

Subproblem 1
Set the factor '(x + -3y)' equal to zero and attempt to solve:

Simplifying
x + -3y = 0

Solving
x + -3y = 0

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

Add '3y' to each side of the equation.
x + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
x + 0 = 0 + 3y
x = 0 + 3y
Remove the zero:
x = 3y

Simplifying
x = 3y
Subproblem 2
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
Solution
x = {3y, -1y}