Please someone help me with this differential equation problems.

Laplace transform question where do these constants come from. I know how to do Laplace transforms with basic identities but I have been having problems now with figuring out where these constants come from. I think its from having to sub in a b and c and then solving but I need someone to show me how. These are the problems L^-1(1/(s^2+s-20) I dont understand where the 1/9 comes from I only get 1/(s-4)(s+5) Also the problem 1/(s-1)^4 this is a shifted prlbem im sure but I cant figure out where they get
1/6 ( 3!/(s-1)^4

Question

Please someone help me with this differential equation problems.

Laplace transform question where do these constants come from. I know how to do Laplace transforms with basic identities but I have been having problems now with figuring out where these constants come from. I think its from having to sub in a b and c and then solving but I need someone to show me how. These are the problems L^-1(1/(s^2+s-20)  I dont understand where the 1/9 comes from I only get 1/(s-4)(s+5)   Also the problem 1/(s-1)^4 this is a shifted prlbem im sure but I cant figure out where they get 
1/6 ( 3!/(s-1)^4