Solve y=2(x-1)(x-m-3)

$$y = 2 ( x - 1 ) ( x - m - 3 )$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=-\frac{-2x^{2}+8x+y-6}{2\left(x-1\right)}\text{, }&x\neq 1\\m\in \mathrm{C}\text{, }&y=0\text{ and }x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$y=\left(2x-2\right)\left(x-m-3\right)$$

Use the distributive property to multiply 2x-2 by x-m-3 and combine like terms.

$$y=2x^{2}-2xm-8x+2m+6$$

Swap sides so that all variable terms are on the left hand side.

$$2x^{2}-2xm-8x+2m+6=y$$

Subtract 2x^{2} from both sides.

$$-2xm-8x+2m+6=y-2x^{2}$$

Add 8x to both sides.

$$-2xm+2m+6=y-2x^{2}+8x$$

Subtract 6 from both sides.

$$-2xm+2m=y-2x^{2}+8x-6$$

Combine all terms containing m.

$$\left(-2x+2\right)m=y-2x^{2}+8x-6$$

The equation is in standard form.

$$\left(2-2x\right)m=-2x^{2}+8x+y-6$$

Divide both sides by -2x+2.

$$\frac{\left(2-2x\right)m}{2-2x}=\frac{-2x^{2}+8x+y-6}{2-2x}$$

Dividing by -2x+2 undoes the multiplication by -2x+2.

$$m=\frac{-2x^{2}+8x+y-6}{2-2x}$$

Divide -2x^{2}+8x+y-6 by -2x+2.

$$m=\frac{-2x^{2}+8x+y-6}{2\left(1-x\right)}$$

Solve for m

$$\left\{\begin{matrix}m=-\frac{-2x^{2}+8x+y-6}{2\left(x-1\right)}\text{, }&x\neq 1\\m\in \mathrm{R}\text{, }&y=0\text{ and }x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$y=\left(2x-2\right)\left(x-m-3\right)$$

Use the distributive property to multiply 2x-2 by x-m-3 and combine like terms.

$$y=2x^{2}-2xm-8x+2m+6$$

Swap sides so that all variable terms are on the left hand side.

$$2x^{2}-2xm-8x+2m+6=y$$

Subtract 2x^{2} from both sides.

$$-2xm-8x+2m+6=y-2x^{2}$$

Add 8x to both sides.

$$-2xm+2m+6=y-2x^{2}+8x$$

Subtract 6 from both sides.

$$-2xm+2m=y-2x^{2}+8x-6$$

Combine all terms containing m.

$$\left(-2x+2\right)m=y-2x^{2}+8x-6$$

The equation is in standard form.

$$\left(2-2x\right)m=-2x^{2}+8x+y-6$$

Divide both sides by -2x+2.

$$\frac{\left(2-2x\right)m}{2-2x}=\frac{-2x^{2}+8x+y-6}{2-2x}$$

Dividing by -2x+2 undoes the multiplication by -2x+2.

$$m=\frac{-2x^{2}+8x+y-6}{2-2x}$$

Divide -2x^{2}+8x+y-6 by -2x+2.

$$m=\frac{-2x^{2}+8x+y-6}{2\left(1-x\right)}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{2y+m^{2}+4m+4}+m+4}{2}$$

$$x=\frac{-\sqrt{2y+m^{2}+4m+4}+m+4}{2}$$

Solve for x

$$x=\frac{\sqrt{2y+m^{2}+4m+4}+m+4}{2}$$

$$x=\frac{-\sqrt{2y+m^{2}+4m+4}+m+4}{2}\text{, }y\geq -\frac{\left(m+2\right)^{2}}{2}$$