The equation lends itself to factoring by grouping.
(x^6 + 36x^4) - (9x^2 + 324) = 0
x^4(x^2 + 36) - 9(x^2 + 36) = 0
(x^4 - 9)(x^2 + 36) = 0
(x^2 - 3)(x^2 + 3)(x^2 + 36) = 0
Solutions are {±√3, ±I√3, ±6i}.
(x^6 + 36x^4) - (9x^2 + 324) = 0
x^4(x^2 + 36) - 9(x^2 + 36) = 0
(x^4 - 9)(x^2 + 36) = 0
(x^2 - 3)(x^2 + 3)(x^2 + 36) = 0
Solutions are {±√3, ±I√3, ±6i}.