6x^2y^2+2xy^2-3y^2=

Solution for 6x^2y^2+2xy^2-3y^2= equation:

Simplifying
6x2y2 + 2xy2 + -3y2 = 0

Reorder the terms:
2xy2 + 6x2y2 + -3y2 = 0

Solving
2xy2 + 6x2y2 + -3y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'y2'.
y2(2x + 6x2 + -3) = 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 '(2x + 6x2 + -3)' equal to zero and attempt to solve:

Simplifying
2x + 6x2 + -3 = 0

Reorder the terms:
-3 + 2x + 6x2 = 0

Solving
-3 + 2x + 6x2 = 0

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
-0.5 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 0.3333333333x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 0.3333333333x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 0.3333333333x + x2 = 0 + 0.5
0.3333333333x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
0.3333333333x + x2 = 0.5

The x term is 0.3333333333x.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333x + 0.02777777779 + x2 = 0.5 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333x + x2 = 0.5 + 0.02777777779

Combine like terms: 0.5 + 0.02777777779 = 0.52777777779
0.02777777779 + 0.3333333333x + x2 = 0.52777777779

Factor a perfect square on the left side:
(x + 0.1666666667)(x + 0.1666666667) = 0.52777777779

Calculate the square root of the right side: 0.726483157

Break this problem into two subproblems by setting 
(x + 0.1666666667) equal to 0.726483157 and -0.726483157.

Subproblem 1
x + 0.1666666667 = 0.726483157

Simplifying
x + 0.1666666667 = 0.726483157

Reorder the terms:
0.1666666667 + x = 0.726483157

Solving
0.1666666667 + x = 0.726483157

Solving for variable 'x'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + x = 0.726483157 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + x = 0.726483157 + -0.1666666667
x = 0.726483157 + -0.1666666667

Combine like terms: 0.726483157 + -0.1666666667 = 0.5598164903
x = 0.5598164903

Simplifying
x = 0.5598164903

Subproblem 2
x + 0.1666666667 = -0.726483157

Simplifying
x + 0.1666666667 = -0.726483157

Reorder the terms:
0.1666666667 + x = -0.726483157

Solving
0.1666666667 + x = -0.726483157

Solving for variable 'x'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + x = -0.726483157 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + x = -0.726483157 + -0.1666666667
x = -0.726483157 + -0.1666666667

Combine like terms: -0.726483157 + -0.1666666667 = -0.8931498237
x = -0.8931498237

Simplifying
x = -0.8931498237

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5598164903, -0.8931498237}
Solution
x = {0.5598164903, -0.8931498237}