Solve nh=-16t^2+1800giv

$$n h = - 16 t ^ { 2 } + 1800 g i v$$

Solve for g

$$\left\{\begin{matrix}g=-\frac{i\left(hn+16t^{2}\right)}{1800v}\text{, }&v\neq 0\\g\in \mathrm{C}\text{, }&\left(n=-\frac{16t^{2}}{h}\text{ and }h\neq 0\text{ and }v=0\right)\text{ or }\left(h=0\text{ and }t=0\text{ and }v=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply 1800 and i to get 1800i.

$$nh=-16t^{2}+1800igv$$

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

$$-16t^{2}+1800igv=nh$$

Add 16t^{2} to both sides.

$$1800igv=nh+16t^{2}$$

The equation is in standard form.

$$1800ivg=hn+16t^{2}$$

Divide both sides by 1800iv.

$$\frac{1800ivg}{1800iv}=\frac{hn+16t^{2}}{1800iv}$$

Dividing by 1800iv undoes the multiplication by 1800iv.

$$g=\frac{hn+16t^{2}}{1800iv}$$

Divide nh+16t^{2} by 1800iv.

$$g=-\frac{i\left(hn+16t^{2}\right)}{1800v}$$

Solve for h

$$\left\{\begin{matrix}h=-\frac{8\left(2t^{2}-225igv\right)}{n}\text{, }&n\neq 0\\h\in \mathrm{C}\text{, }&\left(t=\left(\frac{15}{2}+\frac{15}{2}i\right)\sqrt{g}\sqrt{v}\text{ or }t=\left(-\frac{15}{2}-\frac{15}{2}i\right)\sqrt{g}\sqrt{v}\right)\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply 1800 and i to get 1800i.

$$nh=-16t^{2}+1800igv$$

The equation is in standard form.

$$nh=1800igv-16t^{2}$$

Divide both sides by n.

$$\frac{nh}{n}=\frac{1800igv-16t^{2}}{n}$$

Dividing by n undoes the multiplication by n.

$$h=\frac{1800igv-16t^{2}}{n}$$

Divide -16t^{2}+1800igv by n.

$$h=\frac{8\left(225igv-2t^{2}\right)}{n}$$