Partial Fraction Decomposition for Inverse Laplace Transform

Question

I'm using John Bird's Higher Engineering Mathematics but I'm really struggling with Partial Fraction decomposition. I'm needing to convert it from s domain to t domain using Inverse Laplace Transform. Would really appreciate a bit of guidance, not necessarily looking for the answer but all the examples I have are in a different format and I've hit a brick wall. Thank you.

What I need to use Partial Fraction Decomposition on

Answer 1

First multiply top and bottom by $0.6s$

Then apply partial fraction decomposition to have two fractions instead of one.

Each partial fraction will have $As+B$ or $Cs+D$ on the top and the associated factor in the bottom.