Solve (x+3)(x+m)=x

$$( x + 3 ) ( x + m ) = x$$

Solve for m

$$m=-\frac{x\left(x+2\right)}{x+3}$$

$$x\neq -3$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+3 by x+m.

$$x^{2}+xm+3x+3m=x$$

Subtract x^{2} from both sides.

$$xm+3x+3m=x-x^{2}$$

Subtract 3x from both sides.

$$xm+3m=x-x^{2}-3x$$

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

$$xm+3m=-2x-x^{2}$$

Combine all terms containing m.

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

The equation is in standard form.

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

Divide both sides by x+3.

$$\frac{\left(x+3\right)m}{x+3}=-\frac{x\left(x+2\right)}{x+3}$$

Dividing by x+3 undoes the multiplication by x+3.

$$m=-\frac{x\left(x+2\right)}{x+3}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{m^{2}-8m+4}}{2}-\frac{m}{2}-1$$

$$x=-\frac{\sqrt{m^{2}-8m+4}}{2}-\frac{m}{2}-1$$

Solve for x

$$x=\frac{\sqrt{m^{2}-8m+4}}{2}-\frac{m}{2}-1$$

$$x=-\frac{\sqrt{m^{2}-8m+4}}{2}-\frac{m}{2}-1\text{, }m\geq 2\sqrt{3}+4\text{ or }m\leq 4-2\sqrt{3}$$