MWE:
\documentclass{article}
\usepackage[top=3cm,bottom=3cm,left=3.2cm,right=3.2cm,headsep=10pt,a4paper]{geometry}
\usepackage{amsmath,amsfonts,amssymb,amsthm}
\usepackage{enumitem}
\usepackage{multicol}
\setlength{\columnsep}{1cm}
\setlength{\columnseprule}{1pt}
\allowdisplaybreaks
\begin{document}
\begin{multicols*}{2}
\begin{enumerate}[label=(\alph*)]
\item \begin{align*}
2x+6&=12x-8\\
2x-12x&=-8-6\\
-10x&=-14\\
x&=\dfrac{-14}{-10}\\
&=1\dfrac{2}{5}
\end{align*}
\item \begin{align*}
4x-5&=6(7)\\
&=42\\
4x&=42+5\\
&=47\\
x&=\dfrac{47}{4}\\
&=11\dfrac{3}{4}
\end{align*}
\item \begin{align*}
5(6x-2)&=3(9x+1)\\
30x-10&=27x+3\\
30x-27x&=3+10\\
3x&=13\\
x&=\dfrac{13}{3}\\
&=4\dfrac{1}{3}
\end{align*}
\item \begin{align*}
\dfrac{3(-2x+5)-4(8x+1)}{12}&=7\\
\dfrac{-6x+15-32x-4}{12}&=7\\
\dfrac{-38x+11}{12}&=7
\end{align*}\\
\begin{align*}
-38x+11&=12(7)\\
&=84\\
-38x&=84-11\\
&=73\\
x&=\dfrac{73}{-38}\\
&=-1\dfrac{35}{38}
\end{align*}
\item \begin{align*}
3&=7(x+5)\\
3&=7x+35\\
-7x&=35-3\\
&=32\\
x&=\dfrac{32}{-7}\\
&=-4\dfrac{4}{7}
\end{align*}
\item \begin{align*}
4(5x+6)&=6(3x-2)\\
20x+24&=18x-12\\
20x-18x&=-12-24\\
2x&=-36\\
x&=\dfrac{-36}{2}\\
&=-18
\end{align*}
\end{enumerate}
\end{multicols*}
\end{document}
I am trying to create a solutions page, and would like to remove the vertical space such that (a) is on the same line as the first equation, and there is no vertical space after the last equation, before (b).
Also, the second column shows that LaTex is filling up the entire column with my equations but I would like it to be aligned to the top.
How might I achieve both of these?
Thank you.