I know it can't be factored over the rationals. But I believe it may be factored over the reals into two or four bivaritate polynomials with real coefficients. (from looking at the graph). Or prove it is not possible. (This is one equation written over two lines)
$144y^8-360x^2y^6-2400y^6+297x^4y^4-2160x^2y^4+7504 y^4-90x^6y^2+2070x^4y^2-16040x^2y^2-6080y^2+9x^8- 426x^6+8113x^4-74048x^2+270400$
(Is there a good way to factor polynomials over the reals? Is there some free software to do it?)