Function

we need:
$f(f(x))=x\\ f(x)=f^{-1}(x)$
The only way this is possible is if $f(x)=f^{-1}(x)=x$:
So:
$\cfrac{cx}{(4x-5)(3x+2)}=x\\ \boxed{\displaystyle{c=(4x-5)(3x+2)}}$