We want to find where p(t) = 0 [ no population remains ]
So
0 = -t^4 + 72t^2 + 225 multiply through by -1 and rearrange
t^4 - 72t^2 - 225 = 0 this will factor as
(t^2 - 75) (t^2 + 3) = 0
When set to 0 and solved for t, the second factor produces a non-real answer
For...the first factor we have
t^2 - 75 =0 add 75 to both sides
t^2 = 75 take the positive root
t ≈ 8.66 years
