Solve L=n^2muA/L

$$L = \frac { n ^ { 2 } \mu A } { L }$$

Solve for A

$$A=\frac{\left(\frac{L}{n}\right)^{2}}{\mu }$$

$$\mu \neq 0\text{ and }n\neq 0\text{ and }L\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by L.

$$LL=n^{2}\mu A$$

Multiply L and L to get L^{2}.

$$L^{2}=n^{2}\mu A$$

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

$$n^{2}\mu A=L^{2}$$

The equation is in standard form.

$$\mu n^{2}A=L^{2}$$

Divide both sides by n^{2}\mu .

$$\frac{\mu n^{2}A}{\mu n^{2}}=\frac{L^{2}}{\mu n^{2}}$$

Dividing by n^{2}\mu undoes the multiplication by n^{2}\mu .

$$A=\frac{L^{2}}{\mu n^{2}}$$

Solve for L (complex solution)

$$L=-\sqrt{A}\sqrt{\mu }n$$

$$L=\sqrt{A}\sqrt{\mu }n\text{, }A\neq 0\text{ and }\mu \neq 0\text{ and }n\neq 0$$

Solve for L

$$L=n\sqrt{A\mu }$$

$$L=-n\sqrt{A\mu }\text{, }\left(n\neq 0\text{ and }A<0\text{ and }\mu <0\right)\text{ or }\left(n\neq 0\text{ and }\mu >0\text{ and }A>0\right)$$