Using the method of undetermined coefficients.
Plug into diff eq:
$-3[(Ax+B)e^x]'' - 2[(Ax+B)e^x]' + (Ax+B)e^x = 3xe^x$
Wolfram alpha simplifies this to: $A(x-2)=e^x(4B+3x)$. Solving for A and B we find $A = 3e^3$ and $B = -6/4$.
Thus, we have $y_p = [3xe^3-(6/4)]e^x$ but this is incorrect. What am I doing wrong here?