Before I proceed to write a lot of solutions, I want to adopt a style that I will use consistently in my document. So far I write a solution of an equation as follows. Could you review this ? Any comment, suggestions, improvements to make mine better, more readable, etc are always welcome.
\documentclass[border=12pt,preview]{standalone}
\usepackage{amsmath}
\begin{document}
Solve $-5(1 - 7 x) (3 x + 10) (2 x + 1)=0$ with factorization.
\begin{gather*}
-5(1 - 7 x) (3 x + 10) (2 x + 1)=0\\
1-7x =0 \qquad \text{or}\qquad 3x+10 = 0 \qquad \text{or}\qquad 2x+1=0 \\
-7x =-1 \qquad \text{or}\qquad 3x = -10 \qquad \text{or}\qquad 2x=-1 \\
\begin{aligned}[t]
x &= \frac{-1}{-7}\\
&= \frac{1}{7}
\end{aligned} \qquad \text{or}\qquad
\begin{aligned}[t]
x &= \frac{-10}{3}\\
&= -\frac{10}{3}
\end{aligned}
\qquad \text{or}\qquad
\begin{aligned}[t]
x &= \frac{-1}{2}\\
&= -\frac{1}{2}
\end{aligned}
\end{gather*}
Thus the solution is $x\in \{-\frac{10}{3},-\frac{1}{2},\frac{1}{7}\} $.
\end{document}


=andors are not vertically aligned. So, why not try\begin{align*}and\end{align*}...instead of\begin{gather*}and\end{gather*}? – Partha D. Sep 21 '20 at 08:13