Solve (x-2)(2x-2)-2(2x-2y)=14

$$( x - 2 ) ( 2 x - 2 ) - 2 ( 2 x - 2 y ) = 14$$

Solve for y

$$y=\frac{5+5x-x^{2}}{2}$$

Steps for Solving Linear Equation

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

$$2x^{2}-6x+4-2\left(2x-2y\right)=14$$

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

$$2x^{2}-6x+4-4x+4y=14$$

Combine -6x and -4x to get -10x.

$$2x^{2}-10x+4+4y=14$$

Subtract 2x^{2} from both sides.

$$-10x+4+4y=14-2x^{2}$$

Add 10x to both sides.

$$4+4y=14-2x^{2}+10x$$

Subtract 4 from both sides.

$$4y=14-2x^{2}+10x-4$$

Subtract 4 from 14 to get 10.

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

The equation is in standard form.

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

Divide both sides by 4.

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

Dividing by 4 undoes the multiplication by 4.

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

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

$$y=\frac{5+5x-x^{2}}{2}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{45-8y}+5}{2}$$

$$x=\frac{-\sqrt{45-8y}+5}{2}$$

Solve for x

$$x=\frac{\sqrt{45-8y}+5}{2}$$

$$x=\frac{-\sqrt{45-8y}+5}{2}\text{, }y\leq \frac{45}{8}$$