find the solution set of equation 2x^2-9ix-9=0

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$$\begin{gathered} \mathrm{We} \mathrm{have} \\ 2{\mathrm{x}}^2-9\mathrm{ix}-9=0 \\ \Rightarrow 2{\mathrm{x}}^2-6\mathrm{ix}-3\mathrm{ix}-9=0 \\ \Rightarrow 2{\mathrm{x}}^2-6\mathrm{ix}-3\mathrm{ix}-\frac{9\mathrm{i}}{\mathrm{i}}=0 \\ \Rightarrow 2\mathrm{x}\left(\mathrm{x}-3\mathrm{i}\right)-3\mathrm{i}\left(\mathrm{x}+\frac{3}{\mathrm{i}}\right)=0 \\ \mathrm{Now} \frac{1}{\mathrm{i}}=\frac{\mathrm{i}}{{\mathrm{i}}^2}=-\mathrm{i} \mathrm{As} \left[{\mathrm{i}}^2=-1\right] \\ \mathrm{Hence} \mathrm{above} \mathrm{equation} \mathrm{becomes}, \\ \Rightarrow 2\mathrm{x}\left(\mathrm{x}-3\mathrm{i}\right)-3\mathrm{i}\left(\mathrm{x}-3\mathrm{i}\right)=0 \\ \Rightarrow \left(2\mathrm{x}-3\mathrm{i}\right)\left(\mathrm{x}-3\mathrm{i}\right)=0 \\ \mathrm{Hence} \\ \boxed{\mathbf{x}\mathbf{=}\frac{\mathbf{3}\mathbf{i}}{\mathbf{2}}} \mathrm{or} \boxed{\mathbf{x}\mathbf{=}\mathbf{3}\mathbf{i}} \end{gathered}$$

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