jmc

First, we simplify the left side, and we have $$2^x+2^x+2^x+2^x=4\cdot 2^x=2^2\cdot 2^x=2^{x+2}.$$Noting that $128=2^7$, our equation now is $2^{x+2}=2^7$, so $x+2=7$. Therefore, $x=5$, and $(x+1)(x-1)=(6)(4)=\boxed{24}$.