Find the particular solution of the differential equation
\(6 \frac{\mathrm{~d}^{2} x}{\mathrm{~d} t^{2}}-5 \frac{\mathrm{~d} x}{\mathrm{~d} t}+x=t^{2}+t+1\)
given that, when \(t=0, x=12\) and \(\frac{\mathrm{d} x}{\mathrm{~d} t}=-6\).