Expand $\displaystyle an(n+1)+b(n+1)+c$ to get $\displaystyle an^2+(a+b)n+(b+c)$, now equate this to the polynomial on the LHS. First solve $\displaystyle a$, then $\displaystyle b$, then $\displaystyle c$.
Now you see $\displaystyle a$ should equal 1 to get the right coefficients for $\displaystyle n^2$. Then you should find the other coefficients so the rest of the polynomial equals 0.