Solve x^2+2(m+1)x+3m=0

$$x ^ { 2 } + 2 ( m + 1 ) x + 3 m = 0$$

Solve for m

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

$$x\neq -\frac{3}{2}$$

Steps for Solving Linear Equation

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

$$x^{2}+\left(2m+2\right)x+3m=0$$

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

$$x^{2}+2mx+2x+3m=0$$

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

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

Subtract 2x from both sides.

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

Combine all terms containing m.

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

Divide both sides by 2x+3.

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

Dividing by 2x+3 undoes the multiplication by 2x+3.

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

Solve for x

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

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