[Tex/LaTex] Using \nearrow and \searrow to separate an equation in two alternatives

Question

I'm tryin' to write the solution of an equation with two possible solutions, as x(ax-a+1)=0. I'm using \nearrow and \searrow with an array but I don't get it fits right. This is the code:

$\rightarrow x(ax-a+1)=0\begin{array}{ll}
 & {\color{red}{\color{red}x=0}}\\
\nearrow\\
\searrow & ax-a+1=0\rightarrow x=\dfrac{a-1}{a}\rightarrow{\color{red}{\color{red}x=1-\dfrac{1}{a}}}
\end{array}$

Answer 1

Instead of fixing your approach, I just show two other possibilities which I would prefer here.

% arara: pdflatex

\documentclass{article}
\usepackage{xcolor}
\usepackage{mathtools}
\usepackage{tikz-cd}

\begin{document}
    \[\rightarrow x(ax-a+1)=0\rightarrow\begin{dcases}
    {\color{red}x=0}\\
    ax-a+1=0\rightarrow x=\frac{a-1}{a}\rightarrow{\color{red}x=1-\frac{1}{a}}
    \end{dcases}\]

    \[\begin{tikzcd}[%
    ,row sep={10,between origins}, column sep=15
    ,every arrow/.append style={start anchor=east, end anchor=west}
    ,/tikz/column 2/.append style={anchor=base west}
    ]
    & \color{red}x=0\\
    \rightarrow x(ax-a+1)=0 \arrow{ur}\arrow{dr} & \\
    & ax-a+1=0\rightarrow x=\dfrac{a-1}{a}\rightarrow{\color{red}x=1-\dfrac{1}{a}}
    \end{tikzcd}
    \]
\end{document}

The \rightarrow in front of the big brace is not really needed, though.

If you want to separate the arrows in my second example, you can do something like \arrow[shorten <= 1mm]{ur}\arrow[shorten <= 1mm]{dr} or you add some yshift to their start anchors.