Solve t=n/ar^2

$$t = \frac { n } { a } r ^ { 2 }$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=\frac{at}{r^{2}}\text{, }&a\neq 0\text{ and }r\neq 0\\n\in \mathrm{C}\text{, }&t=0\text{ and }r=0\text{ and }a\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a.

$$ta=nr^{2}$$

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

$$nr^{2}=ta$$

The equation is in standard form.

$$r^{2}n=at$$

Divide both sides by r^{2}.

$$\frac{r^{2}n}{r^{2}}=\frac{at}{r^{2}}$$

Dividing by r^{2} undoes the multiplication by r^{2}.

$$n=\frac{at}{r^{2}}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{nr^{2}}{t}\text{, }&r\neq 0\text{ and }n\neq 0\text{ and }t\neq 0\\a\neq 0\text{, }&\left(r=0\text{ or }n=0\right)\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ta=nr^{2}$$

Divide both sides by t.

$$\frac{ta}{t}=\frac{nr^{2}}{t}$$

Dividing by t undoes the multiplication by t.

$$a=\frac{nr^{2}}{t}$$

Variable a cannot be equal to 0.

$$a=\frac{nr^{2}}{t}\text{, }a\neq 0$$

Solve for n

$$\left\{\begin{matrix}n=\frac{at}{r^{2}}\text{, }&a\neq 0\text{ and }r\neq 0\\n\in \mathrm{R}\text{, }&t=0\text{ and }r=0\text{ and }a\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a.

$$ta=nr^{2}$$

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

$$nr^{2}=ta$$

The equation is in standard form.

$$r^{2}n=at$$

Divide both sides by r^{2}.

$$\frac{r^{2}n}{r^{2}}=\frac{at}{r^{2}}$$

Dividing by r^{2} undoes the multiplication by r^{2}.

$$n=\frac{at}{r^{2}}$$