Solve a+m+2=-(a+m)^2+(m-2)(a+m)+2m

$$a + m + 2 = - ( a + m ) ^ { 2 } + ( m - 2 ) ( a + m ) + 2 m$$

Solve for m (complex solution)

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

Steps for Solving Linear Equation

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+m\right)^{2}.

$$a+m+2=-\left(a^{2}+2am+m^{2}\right)+\left(m-2\right)\left(a+m\right)+2m$$

To find the opposite of a^{2}+2am+m^{2}, find the opposite of each term.

$$a+m+2=-a^{2}-2am-m^{2}+\left(m-2\right)\left(a+m\right)+2m$$

Use the distributive property to multiply m-2 by a+m.

$$a+m+2=-a^{2}-2am-m^{2}+ma+m^{2}-2a-2m+2m$$

Combine -2am and ma to get -am.

$$a+m+2=-a^{2}-am-m^{2}+m^{2}-2a-2m+2m$$

Combine -m^{2} and m^{2} to get 0.

$$a+m+2=-a^{2}-am-2a-2m+2m$$

Combine -2m and 2m to get 0.

$$a+m+2=-a^{2}-am-2a$$

Add am to both sides.

$$a+m+2+am=-a^{2}-2a$$

Subtract a from both sides.

$$m+2+am=-a^{2}-2a-a$$

Combine -2a and -a to get -3a.

$$m+2+am=-a^{2}-3a$$

Subtract 2 from both sides.

$$m+am=-a^{2}-3a-2$$

Combine all terms containing m.

$$\left(1+a\right)m=-a^{2}-3a-2$$

The equation is in standard form.

$$\left(a+1\right)m=-a^{2}-3a-2$$

Divide both sides by 1+a.

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

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

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

Divide -\left(1+a\right)\left(2+a\right) by 1+a.

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

Solve for m

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

Steps for Solving Linear Equation

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+m\right)^{2}.

$$a+m+2=-\left(a^{2}+2am+m^{2}\right)+\left(m-2\right)\left(a+m\right)+2m$$

To find the opposite of a^{2}+2am+m^{2}, find the opposite of each term.

$$a+m+2=-a^{2}-2am-m^{2}+\left(m-2\right)\left(a+m\right)+2m$$

Use the distributive property to multiply m-2 by a+m.

$$a+m+2=-a^{2}-2am-m^{2}+ma+m^{2}-2a-2m+2m$$

Combine -2am and ma to get -am.

$$a+m+2=-a^{2}-am-m^{2}+m^{2}-2a-2m+2m$$

Combine -m^{2} and m^{2} to get 0.

$$a+m+2=-a^{2}-am-2a-2m+2m$$

Combine -2m and 2m to get 0.

$$a+m+2=-a^{2}-am-2a$$

Add am to both sides.

$$a+m+2+am=-a^{2}-2a$$

Subtract a from both sides.

$$m+2+am=-a^{2}-2a-a$$

Combine -2a and -a to get -3a.

$$m+2+am=-a^{2}-3a$$

Subtract 2 from both sides.

$$m+am=-a^{2}-3a-2$$

Combine all terms containing m.

$$\left(1+a\right)m=-a^{2}-3a-2$$

The equation is in standard form.

$$\left(a+1\right)m=-a^{2}-3a-2$$

Divide both sides by 1+a.

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

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

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

Divide -\left(1+a\right)\left(2+a\right) by 1+a.

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

Solve for a

$$a=-1$$

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