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

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

Solve for m

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

$$x\neq 1$$

Steps for Solving Linear Equation

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

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

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

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

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

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

Subtract 2x from both sides.

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

Combine all terms containing m.

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

Divide both sides by x^{2}-2x+1.

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

Dividing by x^{2}-2x+1 undoes the multiplication by x^{2}-2x+1.

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

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

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

Solve for x (complex solution)

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

Solve for x

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