h(t) = -5t^2+165t
We need to set this equation to 450
450 = -5t^2+165t
Subtract 450 from each side
450-450 = -5t^2+165t-450
0 = -5t^2+165t-450
Divide each side by -5
0 = t^2 - 33t+ 90
Now factor the right hand side
0 = ( t-3) (t-30)
Using the zero product property
t-3 =0 t-30 =0
t =3 t=30
t=3 is when it =450 on the way up
t=30 is when it = 450 on the way down
