I am trying to position my equations as in the image below, but I cant seem to get it to work (mainly because I cant get the line breaks to work). How would I position my equation like in the image below? My latex code is below:

\documentclass[11pt,a4paper]{report}
\usepackage{amsmath,amsfonts,amssymb,amsthm,epsfig,epstopdf,titling,url,array}
\theoremstyle{plain}
\newtheorem{thm}{Theorem}[chapter] % reset theorem numbering for each chapter
\newtheorem{lem}[thm]{Lemma}
\newtheorem{prop}[thm]{Proposition}
\newtheorem*{cor}{Corollary}
\theoremstyle{definition}
\newtheorem{defn}[thm]{Definition} % definition numbers are dependent on theorem numbers
\newtheorem{exmp}[thm]{Example} % same for example numbers
\newtheorem{conj}[thm]{Conjecture}
\theoremstyle{remark}
\newtheorem*{rem}{Remark}
\newtheorem*{note}{Note}
\title{My Thesis Title}
\author{My Name}
\date{\today}
\renewcommand\labelenumi{(\theenumi)}
\renewcommand\theenumi{\roman{enumi}}
\begin{document}
\tableofcontents
\chapter{Addition}
\section{Basics}
\begin{defn}
Let $x, y$ be some unknowns, we let:
\begin{equation}
x^2 + y^2 := (x+y)(x-y) := (1+2)(3+4) := (3*7)
= 21
= 42/2
\nonumber
\end{equation}
\end{defn}
\end{document}

*as the multiplication symbol is frowned upon in math circles. – egreg Mar 03 '12 at 16:03\coloneqqfrom themathtoolspackage. http://tex.stackexchange.com/q/4216/9043 – qubyte Mar 03 '12 at 16:05\phantom{:}=. :-| – Werner Mar 03 '12 at 16:05@egreg Thanks, yes the maths is wrong, it was just an (wrong) example. :)
– Gary Mar 03 '12 at 17:29$x^2+y^2=(x+y)(x-y)$students would be very happy. – egreg Mar 03 '12 at 17:34= {} &instead of&=, the{}is needed to make the=spacing correct, but other than that one can easily align to the right instead of to the left. – daleif Mar 03 '12 at 19:01