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

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

Solve for m (complex solution)

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

$$x\neq -i\text{ and }x\neq i$$

Steps for Solving Linear Equation

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

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

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

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

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

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

Add 2x^{2} to both sides.

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

Subtract 2x from both sides.

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

Combine all terms containing m.

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

The equation is in standard form.

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

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

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

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

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

Solve for m

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

Steps for Solving Linear Equation

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

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

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

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

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

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

Add 2x^{2} to both sides.

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

Subtract 2x from both sides.

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

Combine all terms containing m.

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

The equation is in standard form.

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

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

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

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

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

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{-m^{2}+5m-5}-1}{m-2}\text{; }x=-\frac{\sqrt{-m^{2}+5m-5}+1}{m-2}\text{, }&m\neq 2\\x=\frac{1}{2}\text{, }&m=2\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{-m^{2}+5m-5}-1}{m-2}\text{; }x=-\frac{\sqrt{-m^{2}+5m-5}+1}{m-2}\text{, }&m\neq 2\text{ and }m\geq \frac{5-\sqrt{5}}{2}\text{ and }m\leq \frac{\sqrt{5}+5}{2}\\x=\frac{1}{2}\text{, }&m=2\end{matrix}\right.$$