3xy-(2y^2)-x^2=0

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

Simplifying
3xy + -1(2y2) + -1x2 = 0

Remove parenthesis around (2y2)
3xy + -1 * 2y2 + -1x2 = 0

Multiply -1 * 2
3xy + -2y2 + -1x2 = 0

Reorder the terms:
3xy + -1x2 + -2y2 = 0

Solving
3xy + -1x2 + -2y2 = 0

Solving for variable 'x'.

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

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

Simplifying
-1x + y = 0

Solving
-1x + y = 0

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

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

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

Divide each side by '-1'.
x = y

Simplifying
x = y
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 = {y, 2y}