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

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

Solve for m (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply 3m+1 by x.

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

Subtract x from both sides. Anything subtracted from zero gives its negation.

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

Subtract 2 from both sides.

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

Combine all terms containing m.

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

Divide both sides by x^{2}+3x+2.

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

Dividing by x^{2}+3x+2 undoes the multiplication by x^{2}+3x+2.

$$m=\frac{-x-2}{x^{2}+3x+2}$$

Divide -x-2 by x^{2}+3x+2.

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

Solve for m

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

Steps for Solving Linear Equation

Use the distributive property to multiply 3m+1 by x.

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

Subtract x from both sides. Anything subtracted from zero gives its negation.

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

Subtract 2 from both sides.

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

Combine all terms containing m.

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

Divide both sides by x^{2}+3x+2.

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

Dividing by x^{2}+3x+2 undoes the multiplication by x^{2}+3x+2.

$$m=\frac{-x-2}{x^{2}+3x+2}$$

Divide -x-2 by x^{2}+3x+2.

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

Solve for x

$$\left\{\begin{matrix}\\x=-2\text{, }&\text{unconditionally}\\x=-1-\frac{1}{m}\text{, }&m\neq 0\end{matrix}\right.$$