Right-aligned constraints for equation

As you don't need alignment at relation symbols, but centered alignment, you could use an array environment with c columns.

I considered putting two gathered environments next to each other, however, in contrast to an array, alignment of the baselines would not be guaranteed.

If the longest constraint needs to be flushed to the right margin, you could use a tabular* environment with two centered columns; something along these lines (change the lengths according to your needs):

\documentclass[reqno]{amsart}
\usepackage{array}

\newlength\MyIndent
\setlength\MyIndent{10em}

\begin{document}

\vspace{\abovedisplayskip}
\noindent\begin{tabular*}{\textwidth}{@{\hspace{\MyIndent}}>{$}c<{$}@{\extracolsep{\fill}}
    >{$}c<{$}@{}}
  a^2 + b^2 = ab & (a \in \{z,y,x,w,v,u\},\ b \neq 0) \\
  a + b = c & (a \in \{z,y\},\ b = 0) \\
\end{tabular*}\par
\vspace{\belowdisplayskip}

\end{document}

If the longest constraint doesn't need to be flushed to the right margin, a simple array environment will do the job (change the lengths according to your needs):

\documentclass[reqno]{amsart}

\begin{document}

\[
\begin{array}{@{\hspace{7em}}c@{\hspace{3em}}c}
  a^2 + b^2 = ab & (a \in \{z,y,x,w,v,u\},\ b \neq 0) \\
  a + b = c & (a \in \{z,y\},\ b = 0) \\
\end{array}
\]

\end{document}