Solve for f (complex solution)
\left\{\begin{matrix}f=-4\left(\pi \left(-12x^{2}+6\pi x-\pi ^{2}\right)\right)^{-\frac{1}{3}}\sqrt[3]{y}\text{; }f=4e^{\frac{\pi i}{3}}\left(\pi \left(-12x^{2}+6\pi x-\pi ^{2}\right)\right)^{-\frac{1}{3}}\sqrt[3]{y}\text{; }f=4e^{\frac{5\pi i}{3}}\left(\pi \left(-12x^{2}+6\pi x-\pi ^{2}\right)\right)^{-\frac{1}{3}}\sqrt[3]{y}\text{, }&x\neq -\frac{\pi \sqrt{3}i}{12}+\frac{\pi }{4}\text{ and }x\neq \frac{\pi \sqrt{3}i}{12}+\frac{\pi }{4}\\f\in \mathrm{C}\text{, }&\left(x=\frac{\pi \sqrt{3}i}{12}+\frac{\pi }{4}\text{ or }x=-\frac{\pi \sqrt{3}i}{12}+\frac{\pi }{4}\right)\text{ and }y=0\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{\sqrt{\frac{3}{\pi }}\left(\sqrt{f^{3}\left(256y-\left(\pi f\right)^{3}\right)}+\sqrt{3}\pi ^{\frac{3}{2}}f^{3}\right)}{12f^{3}}\text{; }x=\frac{\sqrt{\frac{3}{\pi }}\left(-\sqrt{f^{3}\left(256y-\left(\pi f\right)^{3}\right)}+\sqrt{3}\pi ^{\frac{3}{2}}f^{3}\right)}{12f^{3}}\text{, }&f\neq 0\\x\in \mathrm{C}\text{, }&f=0\text{ and }y=0\end{matrix}\right.
Solve for f
f=-4\sqrt[3]{\frac{y}{\pi \left(-12x^{2}+6\pi x-\pi ^{2}\right)}}
Solve for x
\left\{\begin{matrix}x=\frac{\sqrt{\frac{3}{\pi }}\left(\sqrt{256y-\left(\pi f\right)^{3}}+\sqrt{3}\left(\pi f\right)^{\frac{3}{2}}\right)}{12f^{\frac{3}{2}}}\text{; }x=\frac{\sqrt{\frac{3}{\pi }}\left(-\sqrt{256y-\left(\pi f\right)^{3}}+\sqrt{3}\left(\pi f\right)^{\frac{3}{2}}\right)}{12f^{\frac{3}{2}}}\text{, }&y\geq \frac{\pi ^{3}f^{3}}{256}\text{ and }f>0\\x=\frac{\sqrt{\frac{3}{\pi }}\left(\sqrt{-f^{3}\left(\left(\pi f\right)^{3}-256y\right)}+\sqrt{3}\pi ^{\frac{3}{2}}f^{3}\right)}{12f^{3}}\text{; }x=\frac{\sqrt{\frac{3}{\pi }}\left(-\sqrt{-f^{3}\left(\left(\pi f\right)^{3}-256y\right)}+\sqrt{3}\pi ^{\frac{3}{2}}f^{3}\right)}{12f^{3}}\text{, }&y\leq \frac{\pi ^{3}f^{3}}{256}\text{ and }f<0\\x=\frac{\pi }{4}\text{, }&f=\frac{4\times 2^{\frac{2}{3}}\sqrt[3]{y}}{\pi }\text{ and }y\neq 0\\x\in \mathrm{R}\text{, }&f=0\text{ and }y=0\end{matrix}\right.
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