$$ax^{2}+(4a^{2}-3b)x-12ab=0$$
$\left\{\begin{matrix}\\b=\frac{ax}{3}\text{, }&\text{unconditionally}\\b\in \mathrm{C}\text{, }&a=-\frac{x}{4}\end{matrix}\right.$
$\left\{\begin{matrix}\\b=\frac{ax}{3}\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&a=-\frac{x}{4}\end{matrix}\right.$
$\left\{\begin{matrix}\\a=-\frac{x}{4}\text{, }&\text{unconditionally}\\a=\frac{3b}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&b=0\text{ and }x=0\end{matrix}\right.$
$\left\{\begin{matrix}\\a=-\frac{x}{4}\text{, }&\text{unconditionally}\\a=\frac{3b}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&b=0\text{ and }x=0\end{matrix}\right.$
