Evaluate (complex solution)
\frac{\sqrt{3}\left(-a+\sqrt{3}\right)\left(3a+k\right)}{3}=\frac{\sqrt{3}\left(-2a+\sqrt{3}\right)\left(12a+k\right)}{3}\text{ and }\frac{\sqrt{3}\left(-2a+\sqrt{3}\right)\left(12a+k\right)}{3}=k
Solve for k
\left\{\begin{matrix}k=2\sqrt{3}\text{, }&a=\frac{\sqrt{3}}{3}\\k\in \mathrm{R}\text{, }&a=0\end{matrix}\right.
Solve for a
\left\{\begin{matrix}\\a=0\text{, }&\text{unconditionally}\\a=\frac{\sqrt{3}}{3}\text{, }&k=2\sqrt{3}\end{matrix}\right.
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