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

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

Simplifying
3x2y2 + -1xy2 + -2y2 = 0

Reorder the terms:
-1xy2 + 3x2y2 + -2y2 = 0

Solving
-1xy2 + 3x2y2 + -2y2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
y2((x + -1)(3x + 2)) = 0

Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve:

Simplifying
y2 = 0

Solving
y2 = 0

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

Add '-1y2' to each side of the equation.
y2 + -1y2 = 0 + -1y2
Remove the zero:
0 = -1y2

Simplifying
0 = -1y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(x + -1)' equal to zero and attempt to solve:

Simplifying
x + -1 = 0

Reorder the terms:
-1 + x = 0

Solving
-1 + x = 0

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

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

Combine like terms: -1 + 1 = 0
0 + x = 0 + 1
x = 0 + 1

Combine like terms: 0 + 1 = 1
x = 1

Simplifying
x = 1
Subproblem 3
Set the factor '(3x + 2)' equal to zero and attempt to solve:

Simplifying
3x + 2 = 0

Reorder the terms:
2 + 3x = 0

Solving
2 + 3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {1, -0.6666666667}