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

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

Solve for m (complex solution)

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

Steps for Solving Linear Equation

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

$$mx^{2}+x-2mx+1-3m=0$$

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

$$mx^{2}-2mx+1-3m=-x$$

Subtract 1 from both sides.

$$mx^{2}-2mx-3m=-x-1$$

Combine all terms containing m.

$$\left(x^{2}-2x-3\right)m=-x-1$$

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

$$\frac{\left(x^{2}-2x-3\right)m}{x^{2}-2x-3}=\frac{-x-1}{x^{2}-2x-3}$$

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

$$m=\frac{-x-1}{x^{2}-2x-3}$$

Divide -x-1 by x^{2}-2x-3.

$$m=-\frac{1}{x-3}$$

Solve for m

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

Steps for Solving Linear Equation

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

$$mx^{2}+x-2mx+1-3m=0$$

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

$$mx^{2}-2mx+1-3m=-x$$

Subtract 1 from both sides.

$$mx^{2}-2mx-3m=-x-1$$

Combine all terms containing m.

$$\left(x^{2}-2x-3\right)m=-x-1$$

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

$$\frac{\left(x^{2}-2x-3\right)m}{x^{2}-2x-3}=\frac{-x-1}{x^{2}-2x-3}$$

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

$$m=\frac{-x-1}{x^{2}-2x-3}$$

Divide -x-1 by x^{2}-2x-3.

$$m=-\frac{1}{x-3}$$

Solve for x

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