Solve 3x^4-n^2y+2y^3=0

$$3 x ^ { 4 } - n ^ { 2 } y + 2 y ^ { 3 } = 0$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=-\sqrt{\frac{3x^{4}+2y^{3}}{y}}\text{; }n=\sqrt{\frac{3x^{4}+2y^{3}}{y}}\text{, }&y\neq 0\\n\in \mathrm{C}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Solve for x (complex solution)

$$x=\frac{3^{\frac{3}{4}}i\sqrt[4]{y}\sqrt[4]{n^{2}-2y^{2}}}{3}$$

$$x=\frac{3^{\frac{3}{4}}\sqrt[4]{y}\sqrt[4]{n^{2}-2y^{2}}}{3}$$

$$x=-\frac{3^{\frac{3}{4}}\sqrt[4]{y}\sqrt[4]{n^{2}-2y^{2}}}{3}$$

$$x=-\frac{3^{\frac{3}{4}}i\sqrt[4]{y}\sqrt[4]{n^{2}-2y^{2}}}{3}$$

Solve for n

$$\left\{\begin{matrix}n=\sqrt{\frac{3x^{4}+2y^{3}}{y}}\text{; }n=-\sqrt{\frac{3x^{4}+2y^{3}}{y}}\text{, }&\left(y\neq 0\text{ and }|x|\leq \frac{3^{\frac{3}{4}}\sqrt[4]{-2y^{3}}}{3}\right)\text{ or }y>0\\n\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{3^{\frac{3}{4}}\sqrt{-\sqrt{y\left(n^{2}-2y^{2}\right)}}}{3}\text{; }x=-\frac{3^{\frac{3}{4}}\sqrt{-\sqrt{y\left(n^{2}-2y^{2}\right)}}}{3}\text{, }&\left(n\geq \sqrt{2}y\text{ and }-\sqrt{2}y=|n|\right)\text{ or }\left(y\leq 0\text{ and }|n|=-\sqrt{2}y\right)\text{ or }y=0\text{ or }\left(y\geq 0\text{ and }|n|=\sqrt{2}y\right)\\x=\frac{3^{\frac{3}{4}}\sqrt[4]{y\left(n^{2}-2y^{2}\right)}}{3}\text{; }x=-\frac{3^{\frac{3}{4}}\sqrt[4]{y\left(n^{2}-2y^{2}\right)}}{3}\text{, }&\left(n\geq \sqrt{2}y\text{ and }n\leq -\sqrt{2}y\right)\text{ or }\left(y\geq 0\text{ and }n\leq -\sqrt{2}y\right)\text{ or }\left(y\geq 0\text{ and }n\geq \sqrt{2}y\right)\text{ or }|n|=\sqrt{2}|y|\text{ or }\left(y\leq 0\text{ and }|n|=-\sqrt{2}y\right)\end{matrix}\right.$$