Question asks for laplace transform of
f(t)=t^2 u(t−1)
hint given rewrite in terms of t-1 first

F(t) = t 2 [u(t − 1) − u(t − 2)] − 5[u(t − 2) − u(t − 3)] + (sin t)u(t − 3)

Note that this can be further simplified as:
 f(t) = t 2u(t − 1) − (5 + t 2 )u(t − 2) + (sin t + 5)u(t − 3) 

We would express f(t) as f(t) = f1(t)[u(t − t0) − u(t − t1)] + f2(t)[u(t − t1) − u(t − t2)] + +fn−1(t)[u(t − tn−2) − u(t − tn−1)] + fn(t)u(t − tn−1)

I hope this helps.

First subtract 10 from both side
y^2+6y-16=0
(y+8)(y-2)=0
-8 and 2