Looking for a better layout or style in writing solutions of equations

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 $xin {-frac{10}{3},-frac{1}{2},frac{1}{7}} $.
end{document}

documentclass[border=12pt,preview]{standalone}
usepackage{amsmath}

newcommand{nxt}{&          &&}  %%  next column
newcommand{nxr}{&text{or} &&}  %%  next column with "or" 

begin{document}

Solve $-5(1 - 7 x) (3 x + 10) (2 x + 1)=0$ with  factorization.
%
begin{align*}
-5(1 - 7 x) (3 x + 10) (2 x + 1) = 0
end{align*}
%
begin{align*}
1-7x &=  0            nxr    3x+10 &=   0           nxr      2x+1 &=  0  
 -7x &= -1            nxr    3x    &= -10           nxr      2x   &= -1 
   x &= frac{-1}{-7} nxr     x    &= frac{-10}{3} nxr       x   &= frac{-1}{2} 
     &= frac{1}{7}   nxt          &= -frac{10}{3} nxt           &= -frac{1}{2}
end{align*}
%
Thus the solution is $xin {-frac{10}{3},-frac{1}{2},frac{1}{7}} $.

end{document}