4th Order - Using Method of Undetermined Coeffecients

I'm having trouble with one of my homework problems. The instructions are to use the method of undetermined coefficients to find the particular solution, then form the general solution.

The equation in question is: y''''-3y'''+2y''=3e^(-t) + 6e^(2t) - 6t

I factored the auxiliary equation to get roots of 0 (multiplicity 2),2, and 1 so that:

y1=1

y2=t

y3=e^(2t)

y4=e^t

In forming the undetermined coefficients part of the problem, I have Ae^(-t) + Bte ^(2t) + Ct^2

(Using the modification/multiplication rule)

The problem is that when I find the derivatives of this and plug them back into the equation, most of it cancels out and I get 6Ae^(-t) + 4C = 3e^(-t) + 6e^(2t) - 6t, which does not help me solve for the coefficients. Where am I going wrong here? Thanks!