-3x^4 + 27x^2 + 1200 = 0 multiply through by - 1
3x^4 - 27x^2 - 1200 = 0 divide through by 3
x^4 - 9x^2 - 400 = 0 factor as
(x^2 - 25) ( x^2 + 16) = 0
(x - 5) ( x + 5) (x^2 + 16) = 0
x - 5 = 0 x + 5 = 0 x^2 + 16 = 0
x = 5 x = -5 x^2 = - 16
x = ±√ [-16]
x = ± i√ 16
x = ±4i
The zeroes are -5, 5, 4i, -4i