Solve y=1/3s^2h

$$y = \frac { 1 } { 3 } s ^ { 2 } h$$

Solve for h (complex solution)

$$\left\{\begin{matrix}h=\frac{3y}{s^{2}}\text{, }&s\neq 0\\h\in \mathrm{C}\text{, }&y=0\text{ and }s=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{3}s^{2}h=y$$

The equation is in standard form.

$$\frac{s^{2}}{3}h=y$$

Divide both sides by \frac{1}{3}s^{2}.

$$\frac{3\times \frac{s^{2}}{3}h}{s^{2}}=\frac{3y}{s^{2}}$$

Dividing by \frac{1}{3}s^{2} undoes the multiplication by \frac{1}{3}s^{2}.

$$h=\frac{3y}{s^{2}}$$

Solve for h

$$\left\{\begin{matrix}h=\frac{3y}{s^{2}}\text{, }&s\neq 0\\h\in \mathrm{R}\text{, }&y=0\text{ and }s=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{3}s^{2}h=y$$

The equation is in standard form.

$$\frac{s^{2}}{3}h=y$$

Divide both sides by \frac{1}{3}s^{2}.

$$\frac{3\times \frac{s^{2}}{3}h}{s^{2}}=\frac{3y}{s^{2}}$$

Dividing by \frac{1}{3}s^{2} undoes the multiplication by \frac{1}{3}s^{2}.

$$h=\frac{3y}{s^{2}}$$

Solve for s (complex solution)

$$\left\{\begin{matrix}s=-h^{-\frac{1}{2}}\sqrt{3y}\text{; }s=h^{-\frac{1}{2}}\sqrt{3y}\text{, }&h\neq 0\\s\in \mathrm{C}\text{, }&y=0\text{ and }h=0\end{matrix}\right.$$

Solve for s

$$\left\{\begin{matrix}s=\sqrt{\frac{3y}{h}}\text{; }s=-\sqrt{\frac{3y}{h}}\text{, }&\left(y\geq 0\text{ and }h>0\right)\text{ or }\left(y\leq 0\text{ and }h<0\right)\\s\in \mathrm{R}\text{, }&y=0\text{ and }h=0\end{matrix}\right.$$