I am running into trouble for nicely centering a group of equations in a Mathematics paper written in LaTeX. Say, I want to get the following group of equations 1) written one below another, 2) in the middle of the page to make things look better, 3) with the equality signs one right below the other. For example , say I want to type x^2 - 4 = 0, ( x+2) ( x-2) = 0, x = 2, -2 satisfying the properties 1),2), 3).
a) What packages, and document class should I use ?
b) I need to define any environment before \begin{document}?
c) What are the exact commands that would do the job nicely ?
d) Should I use $$ or just $ ?
e) Also, for the above, can I nicely insert the implication symbol => ?
I tried \\[...]\\, it didn't work for some reason, also tried to include amsmath as a package, and then tried \\begin{align*}....\\end{align*}, didn't work. Also I think I tried $$...$$ and that centered the equation, but not keeping the equality symbols one right below the other, and also changed the output for the equations to a smaller font compared to the rest of the paper.
What exactly should I use that would do the job nicely ? Thanks a lot in advance !

$symbol is reserved and it is used to enter/exit in-line math mode. So you should use$...$to write in-line (i.e., not displayed) math: for example:a function is even if $f(-x)=f(x)$, for all $x$(although the proper LaTeX way would bea function is even if \(f(-x)=f(x)\), for all \(x\)). Never use \ to increase space between paragraphs (See tex.stackexchange.com/q/51722/3954). To end a paragraph, leave a blank line in the code. – Gonzalo Medina May 15 '12 at 02:20