minus 64 from both sides
x⁴-12x²-64=0
hmm
what 2 numbers multiply to -64 and add to get -12
-16 and 4
(x²-16)(x²+4)=0
oh look a difference of 2 perfect squares
(x²-4²)(x²+4)=0
(x-4)(x+4)(x²+4)=0
set each to zero
x-4=0
x=4
x+4=0
x=-4
x²+4=0
x²=-4
if you have learend complex roots then
sqrt both sides to get
x=-2i or 2i
solutions are
x=-4, 4, 2i or -2i