$$t=5+\frac{6}{(z-p)s}$$
$s=-\frac{6}{\left(5-t\right)\left(z-p\right)}$
$z\neq p\text{ and }t\neq 5$
$p=-\frac{6+5sz-stz}{s\left(t-5\right)}$
$t\neq 5\text{ and }s\neq 0$
