Solve (t^2 - 82)^2 = 324 in real numbers.

(t^2 - 82)^2  =  324     expand

t^4  - 164t^2  + 6724  = 324    subtract 324 from borh sides

t^4 - 164t^2  +  6400   =   0     we can factor this as

( t^2  - 100) ( t^2 - 64)  =  0    factor these terms  as differences of squares

(t-10)(t+10)(t-8)(t+8)  =0

Setting each factor to 0  and solving for t  produces  the solutions

t  =10   t  = -10    t  =  8    t  = -8

Thanks!