Solve nh(t)=-5t^2+30t

$$n h ( t ) = - 5 t ^ { 2 } + 30 t$$

Solve for h

$$\left\{\begin{matrix}h=-\frac{5\left(t-6\right)}{n}\text{, }&n\neq 0\\h\in \mathrm{R}\text{, }&t=0\text{ or }\left(t=6\text{ and }n=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$nth=30t-5t^{2}$$

Divide both sides by nt.

$$\frac{nth}{nt}=\frac{5t\left(6-t\right)}{nt}$$

Dividing by nt undoes the multiplication by nt.

$$h=\frac{5t\left(6-t\right)}{nt}$$

Divide 5t\left(6-t\right) by nt.

$$h=\frac{5\left(6-t\right)}{n}$$

Solve for n

$$\left\{\begin{matrix}n=-\frac{5\left(t-6\right)}{h}\text{, }&h\neq 0\\n\in \mathrm{R}\text{, }&t=0\text{ or }\left(t=6\text{ and }h=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$htn=30t-5t^{2}$$

Divide both sides by ht.

$$\frac{htn}{ht}=\frac{5t\left(6-t\right)}{ht}$$

Dividing by ht undoes the multiplication by ht.

$$n=\frac{5t\left(6-t\right)}{ht}$$

Divide 5t\left(6-t\right) by ht.

$$n=\frac{5\left(6-t\right)}{h}$$