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\documentclass[12pt]{article}
\usepackage{hyperref}
\renewcommand{\theequation}{\thesubsection.\arabic{equation}}
\begin{document}
Start Section~1, Subsection~1:
\stepcounter{section}
To square $x$, see: \ref{xsquared}.
\vfil\eject
Another equation is:
\begin{equation}
1+1=2
\end{equation}
Start Subsection~2, with reset equation numbers:
\stepcounter{subsection}
\setcounter{equation}{0}
(Some text.)
\vfil\eject
The square of $x$ is:
\begin{equation}\label{xsquared}
x^2
\end{equation}
\end{document}