Question

$$ax+b=cx+d$$

Solve for a (complex solution)

$\left\{\begin{matrix}a=\frac{cx+d-b}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&b=d\text{ and }x=0\end{matrix}\right.$

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Solve for a

$\left\{\begin{matrix}a=\frac{cx+d-b}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&b=d\text{ and }x=0\end{matrix}\right.$

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Solve for b

$b=cx-ax+d$