Solve operatorname{tn}(x-2)+operatorname{tn}(x+2)=operatorname{tn}45

$$\operatorname { tn } ( x - 2 ) + \operatorname { tn } ( x + 2 ) = \operatorname { tn } 45$$

Solve for n

$$\left\{\begin{matrix}n=\frac{n_{45}}{2x}\text{, }&x\neq 0\\n\in \mathrm{R}\text{, }&\left(n_{45}=0\text{ and }x=0\right)\text{ or }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply tn by x-2.

$$tnx-2tn+tn\left(x+2\right)=tn_{45}$$

Use the distributive property to multiply tn by x+2.

$$tnx-2tn+tnx+2tn=tn_{45}$$

Combine tnx and tnx to get 2tnx.

$$2tnx-2tn+2tn=tn_{45}$$

Combine -2tn and 2tn to get 0.

$$2tnx=tn_{45}$$

The equation is in standard form.

$$2txn=n_{45}t$$

Divide both sides by 2tx.

$$\frac{2txn}{2tx}=\frac{n_{45}t}{2tx}$$

Dividing by 2tx undoes the multiplication by 2tx.

$$n=\frac{n_{45}t}{2tx}$$

Divide tn_{45} by 2tx.

$$n=\frac{n_{45}}{2x}$$

Solve for n_45

$$\left\{\begin{matrix}\\n_{45}=2nx\text{, }&\text{unconditionally}\\n_{45}\in \mathrm{R}\text{, }&t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply tn by x-2.

$$tnx-2tn+tn\left(x+2\right)=tn_{45}$$

Use the distributive property to multiply tn by x+2.

$$tnx-2tn+tnx+2tn=tn_{45}$$

Combine tnx and tnx to get 2tnx.

$$2tnx-2tn+2tn=tn_{45}$$

Combine -2tn and 2tn to get 0.

$$2tnx=tn_{45}$$

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

$$tn_{45}=2tnx$$

The equation is in standard form.

$$tn_{45}=2ntx$$

Divide both sides by t.

$$\frac{tn_{45}}{t}=\frac{2ntx}{t}$$

Dividing by t undoes the multiplication by t.

$$n_{45}=\frac{2ntx}{t}$$

Divide 2tnx by t.

$$n_{45}=2nx$$