4x^4+5x^2y^2-6y^4=

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Solution for 4x^4+5x^2y^2-6y^4= equation: 


Simplifying
4x4 + 5x2y2 + -6y4 = 0

Reorder the terms:
5x2y2 + 4x4 + -6y4 = 0

Solving
5x2y2 + 4x4 + -6y4 = 0

Solving for variable 'x'.

Factor a trinomial.
(4x2 + -3y2)(x2 + 2y2) = 0


Subproblem 1
Set the factor '(4x2 + -3y2)' equal to zero and attempt to solve:

Simplifying
4x2 + -3y2 = 0

Solving
4x2 + -3y2 = 0

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

Add '3y2' to each side of the equation.
4x2 + -3y2 + 3y2 = 0 + 3y2

Combine like terms: -3y2 + 3y2 = 0
4x2 + 0 = 0 + 3y2
4x2 = 0 + 3y2
Remove the zero:
4x2 = 3y2

Divide each side by '4'.
x2 = 0.75y2

Simplifying
x2 = 0.75y2

Take the square root of each side:
x = {-0.866025404y, 0.866025404y}

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

Simplifying
x2 + 2y2 = 0

Solving
x2 + 2y2 = 0

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

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

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

Simplifying
x2 = -2y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {-0.866025404y, 0.866025404y}

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