Solve t=2xL/x^2-n^2

$$t = \frac { 2 x L } { x ^ { 2 } - n ^ { 2 } }$$

Solve for L (complex solution)

$$\left\{\begin{matrix}L=-\frac{t\left(n^{2}-x^{2}\right)}{2x}\text{, }&x\neq 0\text{ and }x\neq n\text{ and }x\neq -n\\L\in \mathrm{C}\text{, }&t=0\text{ and }x=0\text{ and }n\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x+n\right)\left(x-n\right).

$$t\left(x+n\right)\left(x-n\right)=2xL$$

Use the distributive property to multiply t by x+n.

$$\left(tx+tn\right)\left(x-n\right)=2xL$$

Use the distributive property to multiply tx+tn by x-n and combine like terms.

$$tx^{2}-tn^{2}=2xL$$

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

$$2xL=tx^{2}-tn^{2}$$

Divide both sides by 2x.

$$\frac{2xL}{2x}=\frac{t\left(x-n\right)\left(x+n\right)}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$L=\frac{t\left(x-n\right)\left(x+n\right)}{2x}$$

Solve for L

$$\left\{\begin{matrix}L=-\frac{t\left(n^{2}-x^{2}\right)}{2x}\text{, }&x\neq 0\text{ and }|x|\neq |n|\\L\in \mathrm{R}\text{, }&t=0\text{ and }x=0\text{ and }n\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x+n\right)\left(x-n\right).

$$t\left(x+n\right)\left(x-n\right)=2xL$$

Use the distributive property to multiply t by x+n.

$$\left(tx+tn\right)\left(x-n\right)=2xL$$

Use the distributive property to multiply tx+tn by x-n and combine like terms.

$$tx^{2}-tn^{2}=2xL$$

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

$$2xL=tx^{2}-tn^{2}$$

Divide both sides by 2x.

$$\frac{2xL}{2x}=\frac{t\left(x-n\right)\left(x+n\right)}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$L=\frac{t\left(x-n\right)\left(x+n\right)}{2x}$$