Solve y=sqrt{m^2b^3y}

$$y = \sqrt { m ^ { 2 } b ^ { 3 } y }$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=e^{\frac{2\pi i}{3}}m^{-\frac{2}{3}}\sqrt[3]{y}\text{; }b=m^{-\frac{2}{3}}\sqrt[3]{y}\text{; }b=e^{\frac{4\pi i}{3}}m^{-\frac{2}{3}}\sqrt[3]{y}\text{, }&m\neq 0\text{ and }\left(y=0\text{ or }arg(y)<\pi \right)\\b\in \mathrm{C}\text{, }&y=0\end{matrix}\right.$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=-b^{-\frac{3}{2}}\sqrt{y}\text{; }m=b^{-\frac{3}{2}}\sqrt{y}\text{, }&b\neq 0\text{ and }\left(y=0\text{ or }arg(y)<\pi \right)\\m\in \mathrm{C}\text{, }&y=0\end{matrix}\right.$$

Solve for b

$$\left\{\begin{matrix}b=\frac{\sqrt[3]{y}}{m^{\frac{2}{3}}}\text{, }&y\geq 0\text{ and }m\neq 0\\b\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$

Solve for m

$$\left\{\begin{matrix}m=\sqrt{\frac{y}{b^{3}}}\text{; }m=-\sqrt{\frac{y}{b^{3}}}\text{, }&\left(y\geq 0\text{ and }b>0\right)\text{ or }\left(y=0\text{ and }b\neq 0\right)\\m\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$