Solve x^2+(m+1)x-m-2=0

$$x ^ { 2 } + ( m + 1 ) x - m - 2 = 0$$

Solve for m (complex solution)

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

Steps for Solving Linear Equation

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

$$x^{2}+mx+x-m-2=0$$

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$mx+x-m-2=-x^{2}$$

Subtract x from both sides.

$$mx-m-2=-x^{2}-x$$

Add 2 to both sides.

$$mx-m=-x^{2}-x+2$$

Combine all terms containing m.

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

The equation is in standard form.

$$\left(x-1\right)m=2-x-x^{2}$$

Divide both sides by -1+x.

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

Dividing by -1+x undoes the multiplication by -1+x.

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

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

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

Solve for m

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

Steps for Solving Linear Equation

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

$$x^{2}+mx+x-m-2=0$$

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$mx+x-m-2=-x^{2}$$

Subtract x from both sides.

$$mx-m-2=-x^{2}-x$$

Add 2 to both sides.

$$mx-m=-x^{2}-x+2$$

Combine all terms containing m.

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

The equation is in standard form.

$$\left(x-1\right)m=2-x-x^{2}$$

Divide both sides by -1+x.

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

Dividing by -1+x undoes the multiplication by -1+x.

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

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

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

Solve for x

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

$$x=1$$