x^4-5x^2y^2-36y^4=0

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Solution for x^4-5x^2y^2-36y^4=0 equation: 


Simplifying
x4 + -5x2y2 + -36y4 = 0

Reorder the terms:
-5x2y2 + x4 + -36y4 = 0

Solving
-5x2y2 + x4 + -36y4 = 0

Solving for variable 'x'.

Factor a trinomial.
(x2 + -9y2)(x2 + 4y2) = 0

Factor a difference between two squares.
((x + 3y)(x + -3y))(x2 + 4y2) = 0


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

Simplifying
x2 + 4y2 = 0

Solving
x2 + 4y2 = 0

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

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

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

Simplifying
x2 = -4y2

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 + 3y)' equal to zero and attempt to solve:

Simplifying
x + 3y = 0

Solving
x + 3y = 0

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

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

Combine like terms: 3y + -3y = 0
x + 0 = 0 + -3y
x = 0 + -3y
Remove the zero:
x = -3y

Simplifying
x = -3y

Subproblem 3
Set the factor '(x + -3y)' equal to zero and attempt to solve:

Simplifying
x + -3y = 0

Solving
x + -3y = 0

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

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

Combine like terms: -3y + 3y = 0
x + 0 = 0 + 3y
x = 0 + 3y
Remove the zero:
x = 3y

Simplifying
x = 3y
Solution
x = {-3y, 3y}

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