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}.