If C(20, n+2)=C(20, n-2) , then what is n equal to?

$\binom{20}{(n+2)}=\binom{20}{(n-2)}\Rightarrow \frac{20!}{(n+2)!(20-n-2)!}=\frac{20!}{(n-2)!(20-n+2)!}$$\begin{aligned} & \Rightarrow \frac{(22-n)!}{(18-n)!}=\frac{(n+2)!}{(n-2)!} \\ & \Rightarrow(22-n)(21-n)(20-n)(19-n) \\ & \quad=(n+2)(n+1) \cdot n \cdot(n-1)\end{aligned}$For $n=10\begin{aligned} & (22-10)(21-10)(20-10)(19-10) \\ & =(10+2)(10+1) \cdot 10 \cdot(10-1) \\ & \Rightarrow 12 \cdot 11 \cdot 10 \cdot 9=12 \cdot 11 \cdot 10 \cdot 9 \end{aligned}$$$Hence,$n=10$.