6x^4+7x^2y^2-3y^4=

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Solution for 6x^4+7x^2y^2-3y^4= equation: 


Simplifying
6x4 + 7x2y2 + -3y4 = 0

Reorder the terms:
7x2y2 + 6x4 + -3y4 = 0

Solving
7x2y2 + 6x4 + -3y4 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x2 + -1y2)(2x2 + 3y2) = 0


Subproblem 1
Set the factor '(3x2 + -1y2)' equal to zero and attempt to solve:

Simplifying
3x2 + -1y2 = 0

Solving
3x2 + -1y2 = 0

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

Add 'y2' to each side of the equation.
3x2 + -1y2 + y2 = 0 + y2

Combine like terms: -1y2 + y2 = 0
3x2 + 0 = 0 + y2
3x2 = 0 + y2
Remove the zero:
3x2 = y2

Divide each side by '3'.
x2 = 0.3333333333y2

Simplifying
x2 = 0.3333333333y2

Take the square root of each side:
x = {-0.577350269y, 0.577350269y}

Subproblem 2
Set the factor '(2x2 + 3y2)' equal to zero and attempt to solve:

Simplifying
2x2 + 3y2 = 0

Solving
2x2 + 3y2 = 0

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

Add '-3y2' to each side of the equation.
2x2 + 3y2 + -3y2 = 0 + -3y2

Combine like terms: 3y2 + -3y2 = 0
2x2 + 0 = 0 + -3y2
2x2 = 0 + -3y2
Remove the zero:
2x2 = -3y2

Divide each side by '2'.
x2 = -1.5y2

Simplifying
x2 = -1.5y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {-0.577350269y, 0.577350269y}

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