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You are probably right that there are better ways, but I appreciate your help nonetheless. Many thanks!

I see, thank you. I'm still pretty new to LaTeX. I guess as a follow-up question (not that it is necessary any more, since it looks fine without it) I would like to ask how do I keep the exceptionally long lines from going to the left of the equal sign?

That is, after removing the superfluous ...

I have the standard math packages (amsmath, etc), but I was running into trouble trying to use the following code:

\begin{align*}
w &=& f(z,w) \\
&=& z^3 + (a_1z + a_2z^2)w + (a_3 + a_4z)w^2 + a_6w^3 \\
&=& z^3 + (a_1z + a_2z^2)f(z,w) + (a_3 + a_4z)f(z,w)^2 + a_6f(z,w)^3 \\
&=& z^3 + (a_1z + a_2z ...