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

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

Solve for m

$$m=-\frac{x^{2}-2x-2}{x-1}$$

$$x\neq 1$$

Steps for Solving Linear Equation

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

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

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

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

Subtract 2m from both sides.

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

Combine m and -2m to get -m.

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

Subtract x^{2} from both sides.

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

Combine all terms containing m.

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

Divide both sides by x-1.

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

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

$$m=\frac{2+2x-x^{2}}{x-1}$$

Solve for x

$$x=\frac{\sqrt{m^{2}+12}}{2}-\frac{m}{2}+1$$

$$x=-\frac{\sqrt{m^{2}+12}}{2}-\frac{m}{2}+1$$