I don't really understand how to start this question, can anyone help please?

For with , the Laguerre differential equation

Has the solution for which

Prove that the Laplace tranform on is

Hence find the Laplace transform of and deduce the value of

Can someone please help me or even give me a push in the right direction, please, I'm really really stuck!! I have spent days trying to make a start but I really don't understand where to start!!!