Solve (x-10)(x-1)--(x+1)(x-y)=6

$$(x-10)(x-1)--(x+1)(x-y)=6$$

Solve for y

$$y=\frac{2\left(x^{2}-5x+2\right)}{x+1}$$

$$x\neq -1$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-10 by x-1 and combine like terms.

$$x^{2}-11x+10-\left(-\left(x+1\right)\right)\left(x-y\right)=6$$

To find the opposite of x+1, find the opposite of each term.

$$x^{2}-11x+10-\left(-x-1\right)\left(x-y\right)=6$$

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

$$x^{2}-11x+10-\left(-x^{2}+xy-x+y\right)=6$$

To find the opposite of -x^{2}+xy-x+y, find the opposite of each term.

$$x^{2}-11x+10+x^{2}-xy+x-y=6$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}-11x+10-xy+x-y=6$$

Combine -11x and x to get -10x.

$$2x^{2}-10x+10-xy-y=6$$

Subtract 2x^{2} from both sides.

$$-10x+10-xy-y=6-2x^{2}$$

Add 10x to both sides.

$$10-xy-y=6-2x^{2}+10x$$

Subtract 10 from both sides.

$$-xy-y=6-2x^{2}+10x-10$$

Subtract 10 from 6 to get -4.

$$-xy-y=-4-2x^{2}+10x$$

Combine all terms containing y.

$$\left(-x-1\right)y=-4-2x^{2}+10x$$

The equation is in standard form.

$$\left(-x-1\right)y=-2x^{2}+10x-4$$

Divide both sides by -x-1.

$$\frac{\left(-x-1\right)y}{-x-1}=\frac{-2x^{2}+10x-4}{-x-1}$$

Dividing by -x-1 undoes the multiplication by -x-1.

$$y=\frac{-2x^{2}+10x-4}{-x-1}$$

Divide -4-2x^{2}+10x by -x-1.

$$y=-\frac{2\left(-x^{2}+5x-2\right)}{x+1}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{y^{2}+28y+68}+y+10}{4}$$

$$x=\frac{-\sqrt{y^{2}+28y+68}+y+10}{4}$$

Solve for x

$$x=\frac{\sqrt{y^{2}+28y+68}+y+10}{4}$$

$$x=\frac{-\sqrt{y^{2}+28y+68}+y+10}{4}\text{, }y\geq 8\sqrt{2}-14\text{ or }y\leq -8\sqrt{2}-14$$