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

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

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{3}{x+2}\text{, }&x\neq -2\\m\in \mathrm{C}\text{, }&x=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

Add 3x to both sides. Anything plus zero gives itself.

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

Add 3 to both sides.

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

Combine all terms containing m.

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

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

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

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

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

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

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

Solve for m

$$\left\{\begin{matrix}m=\frac{3}{x+2}\text{, }&x\neq -2\\m\in \mathrm{R}\text{, }&x=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

Add 3x to both sides. Anything plus zero gives itself.

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

Add 3 to both sides.

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

Combine all terms containing m.

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

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

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

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

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

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

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

Solve for x

$$\left\{\begin{matrix}\\x=-1\text{, }&\text{unconditionally}\\x=-2+\frac{3}{m}\text{, }&m\neq 0\end{matrix}\right.$$