My 2006 DTS shakes when driving over 65 what does that mean

What is your question?

When driving fast I notice that the car shakes makes a rattling noise and when stopping g it makes a thomping noise

What makes this problem better or worse?

When driving g if I turn the wheel slightly to the right the car rides good

How long has your 2006 Cadillac DTS had this problem?

Since I bought the car 3weeks ago