second-order difference equation (hypergeometric type equation)

Question

We defined the backward and forward difference operators ($\Delta$ and $\nabla$ respectively) by $\Delta f(x)=f(x+1)-f(x)$ and $\nabla f(x)=f(x)-f(x-1)$. We consider the following equation $$ -B(x)f(x+1)+[B(x)+D(x)]f(x)-D(x)f(x−1)+n(n+\mu +\nu +1)f(x) =0,\qquad (*) $$ where $B(x) = (x+\mu +1)(x−N)$ and $D(x) = x(x−\nu −N −1)$. I want to show that : $$ x(N + \mu - x)\Delta\nabla f(x) +[(\nu + 1)(N - 1) -(\mu +\nu + 2)x] \Delta f(x) + n(n +\mu+ \nu + 1)f(x) = 0, $$ I tried the following steps but I didn't find the desired result: $$ (*)\Leftrightarrow -B(x)[f(x+1)-f(x)]+D(x)[f(x)-f(x−1)]+n(n+\mu +\nu +1)f(x) =0, $$ then $$ (*)\Leftrightarrow -B(x)\Delta f(x)+D(x)\nabla f(x)+ n(n+\mu +\nu +1)f(x) =0, $$ An idea please.