Break equation in parts

After removing all unnecessary brackets, correcting size of used ones, with use nccmath for medium size fractions and changed lines of equation:

\documentclass{article}
\usepackage{nccmath}
%---------------- show page layout. don't use in a real document!
\usepackage{showframe}
\renewcommand\ShowFrameLinethickness{0.15pt}
\renewcommand*\ShowFrameColor{\color{red}}

\begin{document}
\begin{multline*}
P_t=
 \frac{1}{2}\Biggl(m_t+v_t-u_t           \\
    + \frac{1-\zeta }{2}\frac{E_{t-1}m_t 
    + \mfrac{1-\zeta}{2\zeta}E_{t-2}m_t
    + \mfrac{\zeta(1-\zeta)}{2(1+\zeta)}E_{t-2}P_{t-1}
    + \mfrac{\zeta}{2}P_{t-1} 
    + \mfrac{\zeta}{1+\zeta}P_{t-2}}
           {1+\zeta}\Biggr)                \\
+ \frac{1-\zeta}{4}
  \frac{E_{t-2}m_t + \frac{\zeta}{2}(E_{t-2}P_{t-1} 
    + P_{t-2})}{1+\zeta}  
    + \frac{\zeta }{4}\Bigl(P_{t-1}+P_{t-2}\Bigr)
\end{multline*}
\end{document}

(red lines indicate text borders)

I would simplify the formula first and then typeset it across three rows using an align* environment.

\documentclass{article}
\usepackage{amsmath}
\DeclareMathOperator{\E}{E}  % expectations operator

\begin{document}
\begin{align*}
P_t
&=\frac{1}{2}(m_t+v_t-u_t)
 +\frac{1}{4}\frac{1-\zeta}{1+\zeta}
  \biggl[\E_{t-1}m_t +\frac{1-\zeta}{2\zeta }\E_{t-2}m_t\\
&\quad +\frac{\zeta (1-\zeta)}{2(1+\zeta)}\E_{t-2}P_{t-1}
 +\frac{\zeta}{2}P_{t-1}+\frac{\zeta}{1+\zeta }P_{t-2}
 +\E_{t-2}m_t\\
&\quad +\frac{\zeta}{2} (\E_{t-2}P_{t-1}+P_{t-2})\biggr]
 +\frac{1}{4}\zeta (P_{t-1}+P_{t-2})
\end{align*}
\end{document}