x^4+18y^4-(3xy)(3xy)=0

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Solution for x^4+18y^4-(3xy)(3xy)=0 equation: 


Simplifying
x4 + 18y4 + -1(3xy)(3xy) = 0

Remove parenthesis around (3xy)
x4 + 18y4 + -1 * 3xy(3xy) = 0

Remove parenthesis around (3xy)
x4 + 18y4 + -1 * 3xy * 3xy = 0

Reorder the terms for easier multiplication:
x4 + 18y4 + -1 * 3 * 3xy * xy = 0

Multiply -1 * 3
x4 + 18y4 + -3 * 3xy * xy = 0

Multiply -3 * 3
x4 + 18y4 + -9xy * xy = 0

Multiply xy * xy
x4 + 18y4 + -9x2y2 = 0

Reorder the terms:
-9x2y2 + x4 + 18y4 = 0

Solving
-9x2y2 + x4 + 18y4 = 0

Solving for variable 'x'.

Factor a trinomial.
(x2 + -6y2)(x2 + -3y2) = 0


Subproblem 1
Set the factor '(x2 + -6y2)' equal to zero and attempt to solve:

Simplifying
x2 + -6y2 = 0

Solving
x2 + -6y2 = 0

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

Add '6y2' to each side of the equation.
x2 + -6y2 + 6y2 = 0 + 6y2

Combine like terms: -6y2 + 6y2 = 0
x2 + 0 = 0 + 6y2
x2 = 0 + 6y2
Remove the zero:
x2 = 6y2

Simplifying
x2 = 6y2

Take the square root of each side:
x = {-2.449489743y, 2.449489743y}

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

Simplifying
x2 + -3y2 = 0

Solving
x2 + -3y2 = 0

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

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

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

Simplifying
x2 = 3y2

Take the square root of each side:
x = {-1.732050808y, 1.732050808y}
Solution
x = {-2.449489743y, 2.449489743y, -1.732050808y, 1.732050808y}

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