Solve h=v_t^2-v_0^2/2*g

$$h = \frac { v _ { t } ^ { 2 } - v _ { 0 } ^ { 2 } } { 2 \cdot g }$$

Solve for g

$$\left\{\begin{matrix}g=\frac{v_{t}^{2}}{2\left(v_{0}^{2}+h\right)}\text{, }&v_{t}\neq 0\text{ and }h\neq -v_{0}^{2}\\g\neq 0\text{, }&v_{t}=0\text{ and }h=-v_{0}^{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable g cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2g.

$$h\times 2g=v_{t}^{2}-v_{0}^{2}\times 2g$$

Add v_{0}^{2}\times 2g to both sides.

$$h\times 2g+v_{0}^{2}\times 2g=v_{t}^{2}$$

Combine all terms containing g.

$$\left(h\times 2+v_{0}^{2}\times 2\right)g=v_{t}^{2}$$

The equation is in standard form.

$$\left(2v_{0}^{2}+2h\right)g=v_{t}^{2}$$

Divide both sides by 2v_{0}^{2}+2h.

$$\frac{\left(2v_{0}^{2}+2h\right)g}{2v_{0}^{2}+2h}=\frac{v_{t}^{2}}{2v_{0}^{2}+2h}$$

Dividing by 2v_{0}^{2}+2h undoes the multiplication by 2v_{0}^{2}+2h.

$$g=\frac{v_{t}^{2}}{2v_{0}^{2}+2h}$$

Divide v_{t}^{2} by 2v_{0}^{2}+2h.

$$g=\frac{v_{t}^{2}}{2\left(v_{0}^{2}+h\right)}$$

Variable g cannot be equal to 0.

$$g=\frac{v_{t}^{2}}{2\left(v_{0}^{2}+h\right)}\text{, }g\neq 0$$

Solve for h

$$h=-v_{0}^{2}+\frac{v_{t}^{2}}{2g}$$

$$g\neq 0$$