Solve 1/2v^2=gh

$$\frac { 1 } { 2 } v ^ { 2 } = g h$$

Solve for g (complex solution)

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

Steps for Solving Linear Equation

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

$$gh=\frac{1}{2}v^{2}$$

The equation is in standard form.

$$hg=\frac{v^{2}}{2}$$

Divide both sides by h.

$$\frac{hg}{h}=\frac{v^{2}}{2h}$$

Dividing by h undoes the multiplication by h.

$$g=\frac{v^{2}}{2h}$$

Solve for h (complex solution)

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

Steps for Solving Linear Equation

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

$$gh=\frac{1}{2}v^{2}$$

The equation is in standard form.

$$gh=\frac{v^{2}}{2}$$

Divide both sides by g.

$$\frac{gh}{g}=\frac{v^{2}}{2g}$$

Dividing by g undoes the multiplication by g.

$$h=\frac{v^{2}}{2g}$$

Solve for g

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

Steps for Solving Linear Equation

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

$$gh=\frac{1}{2}v^{2}$$

The equation is in standard form.

$$hg=\frac{v^{2}}{2}$$

Divide both sides by h.

$$\frac{hg}{h}=\frac{v^{2}}{2h}$$

Dividing by h undoes the multiplication by h.

$$g=\frac{v^{2}}{2h}$$

Solve for h

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

Steps for Solving Linear Equation

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

$$gh=\frac{1}{2}v^{2}$$

The equation is in standard form.

$$gh=\frac{v^{2}}{2}$$

Divide both sides by g.

$$\frac{gh}{g}=\frac{v^{2}}{2g}$$

Dividing by g undoes the multiplication by g.

$$h=\frac{v^{2}}{2g}$$