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

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

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

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

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

Solving for variable 'x'.

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

Ignore the factor 2.
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 '(-1x + 3x2 + -3)' equal to zero and attempt to solve:

Simplifying
-1x + 3x2 + -3 = 0

Reorder the terms:
-3 + -1x + 3x2 = 0

Solving
-3 + -1x + 3x2 = 0

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

Divide each side by '3'.
-1 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.3333333333x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -0.3333333333x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.3333333333x + x2 = 0 + 1
-0.3333333333x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-0.3333333333x + x2 = 1

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 = 1 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = 1 + 0.02777777779

Combine like terms: 1 + 0.02777777779 = 1.02777777779
0.02777777779 + -0.3333333333x + x2 = 1.02777777779

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = 1.02777777779

Calculate the square root of the right side: 1.013793755

Break this problem into two subproblems by setting 
(x + -0.1666666667) equal to 1.013793755 and -1.013793755.

Subproblem 1
x + -0.1666666667 = 1.013793755

Simplifying
x + -0.1666666667 = 1.013793755

Reorder the terms:
-0.1666666667 + x = 1.013793755

Solving
-0.1666666667 + x = 1.013793755

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 = 1.013793755 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = 1.013793755 + 0.1666666667
x = 1.013793755 + 0.1666666667

Combine like terms: 1.013793755 + 0.1666666667 = 1.1804604217
x = 1.1804604217

Simplifying
x = 1.1804604217

Subproblem 2
x + -0.1666666667 = -1.013793755

Simplifying
x + -0.1666666667 = -1.013793755

Reorder the terms:
-0.1666666667 + x = -1.013793755

Solving
-0.1666666667 + x = -1.013793755

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 = -1.013793755 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = -1.013793755 + 0.1666666667
x = -1.013793755 + 0.1666666667

Combine like terms: -1.013793755 + 0.1666666667 = -0.8471270883
x = -0.8471270883

Simplifying
x = -0.8471270883

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.1804604217, -0.8471270883}
Solution
x = {1.1804604217, -0.8471270883}