How do I find the ROC of a system if it has no poles
Since your time domain equation is of finite length, its Z-transform sum converges for (almost) any given $z$. Hence, the ROC of your system function spans the entire complex plane except for 


$z=0$, which is included only if your function is anti-causal and contains only negative potencies $z^{-n}$ which evaluate as $\frac{1}{z^n} \to \infty$ for $z=0$, or
$|z| = \infty$, which will only be in the ROC for purely causal functions. Causal components $z^n$ will approach infinite values when $z$ is $\pm\infty$ (or any complex number of infinite radius), hence the absolute value.


Since your function has both causal and anti-causal parts, the sequence converges for $0 &lt; |z| &lt; \infty$. The region is limited by the two poles at $z=0$ and $|z|=\infty$.