Never thought about doing the question like that but lets roll with it...

If x=5, everything bu the A term is 0 so we get...

216A = 216.

So A = 1.

If x=-1, everything but the D term cancels and you get...

-6D = -12, D = 2

Now set x to be something generic like 0.

Chances are you'll get something like ...B + ...C = -9

Then set x to be something else. Like 1 for example.

Once again you'll get an equation involving B and C.

Solve for B and C using simultaneous equations.