Solve A_{m}=x_{m}*(18n-x_{n}-x_{n})

$$A _ { m } = x _ { m } \cdot ( 18 n - x _ { n } - x _ { n } )$$

Solve for n

$$\left\{\begin{matrix}n=\frac{x_{n}}{9}+\frac{A_{m}}{18x_{m}}\text{, }&x_{m}\neq 0\\n\in \mathrm{R}\text{, }&A_{m}=0\text{ and }x_{m}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine -x_{n} and -x_{n} to get -2x_{n}.

$$A_{m}=x_{m}\left(18n-2x_{n}\right)$$

Use the distributive property to multiply x_{m} by 18n-2x_{n}.

$$A_{m}=18x_{m}n-2x_{m}x_{n}$$

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

$$18x_{m}n-2x_{m}x_{n}=A_{m}$$

Add 2x_{m}x_{n} to both sides.

$$18x_{m}n=A_{m}+2x_{m}x_{n}$$

The equation is in standard form.

$$18x_{m}n=2x_{m}x_{n}+A_{m}$$

Divide both sides by 18x_{m}.

$$\frac{18x_{m}n}{18x_{m}}=\frac{2x_{m}x_{n}+A_{m}}{18x_{m}}$$

Dividing by 18x_{m} undoes the multiplication by 18x_{m}.

$$n=\frac{2x_{m}x_{n}+A_{m}}{18x_{m}}$$

Divide A_{m}+2x_{m}x_{n} by 18x_{m}.

$$n=\frac{x_{n}}{9}+\frac{A_{m}}{18x_{m}}$$

Solve for A_m

$$A_{m}=2x_{m}\left(9n-x_{n}\right)$$