Solve n(m+2)+2(m+1)=m

$$n ( m + 2 ) + 2 ( m + 1 ) = m$$

Solve for m (complex solution)

$$\left\{\begin{matrix}\\m=-2\text{, }&\text{unconditionally}\\m\in \mathrm{C}\text{, }&n=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply n by m+2.

$$nm+2n+2\left(m+1\right)=m$$

Use the distributive property to multiply 2 by m+1.

$$nm+2n+2m+2=m$$

Subtract m from both sides.

$$nm+2n+2m+2-m=0$$

Combine 2m and -m to get m.

$$nm+2n+m+2=0$$

Subtract 2n from both sides. Anything subtracted from zero gives its negation.

$$nm+m+2=-2n$$

Subtract 2 from both sides.

$$nm+m=-2n-2$$

Combine all terms containing m.

$$\left(n+1\right)m=-2n-2$$

Divide both sides by 1+n.

$$\frac{\left(n+1\right)m}{n+1}=\frac{-2n-2}{n+1}$$

Dividing by 1+n undoes the multiplication by 1+n.

$$m=\frac{-2n-2}{n+1}$$

Divide -2n-2 by 1+n.

$$m=-2$$

Solve for n (complex solution)

$$\left\{\begin{matrix}\\n=-1\text{, }&\text{unconditionally}\\n\in \mathrm{C}\text{, }&m=-2\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply n by m+2.

$$nm+2n+2\left(m+1\right)=m$$

Use the distributive property to multiply 2 by m+1.

$$nm+2n+2m+2=m$$

Subtract 2m from both sides.

$$nm+2n+2=m-2m$$

Combine m and -2m to get -m.

$$nm+2n+2=-m$$

Subtract 2 from both sides.

$$nm+2n=-m-2$$

Combine all terms containing n.

$$\left(m+2\right)n=-m-2$$

Divide both sides by 2+m.

$$\frac{\left(m+2\right)n}{m+2}=\frac{-m-2}{m+2}$$

Dividing by 2+m undoes the multiplication by 2+m.

$$n=\frac{-m-2}{m+2}$$

Divide -m-2 by 2+m.

$$n=-1$$

Solve for m

$$\left\{\begin{matrix}\\m=-2\text{, }&\text{unconditionally}\\m\in \mathrm{R}\text{, }&n=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply n by m+2.

$$nm+2n+2\left(m+1\right)=m$$

Use the distributive property to multiply 2 by m+1.

$$nm+2n+2m+2=m$$

Subtract m from both sides.

$$nm+2n+2m+2-m=0$$

Combine 2m and -m to get m.

$$nm+2n+m+2=0$$

Subtract 2n from both sides. Anything subtracted from zero gives its negation.

$$nm+m+2=-2n$$

Subtract 2 from both sides.

$$nm+m=-2n-2$$

Combine all terms containing m.

$$\left(n+1\right)m=-2n-2$$

Divide both sides by 1+n.

$$\frac{\left(n+1\right)m}{n+1}=\frac{-2n-2}{n+1}$$

Dividing by 1+n undoes the multiplication by 1+n.

$$m=\frac{-2n-2}{n+1}$$

Divide -2n-2 by 1+n.

$$m=-2$$

Solve for n

$$\left\{\begin{matrix}\\n=-1\text{, }&\text{unconditionally}\\n\in \mathrm{R}\text{, }&m=-2\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply n by m+2.

$$nm+2n+2\left(m+1\right)=m$$

Use the distributive property to multiply 2 by m+1.

$$nm+2n+2m+2=m$$

Subtract 2m from both sides.

$$nm+2n+2=m-2m$$

Combine m and -2m to get -m.

$$nm+2n+2=-m$$

Subtract 2 from both sides.

$$nm+2n=-m-2$$

Combine all terms containing n.

$$\left(m+2\right)n=-m-2$$

Divide both sides by 2+m.

$$\frac{\left(m+2\right)n}{m+2}=\frac{-m-2}{m+2}$$

Dividing by 2+m undoes the multiplication by 2+m.

$$n=\frac{-m-2}{m+2}$$

Divide -m-2 by 2+m.

$$n=-1$$