Solve 2(x-3)(y-3)+3=x

$$2(x-3)(y-3)+3=x$$

Solve for x

$$\left\{\begin{matrix}\\x=3\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=\frac{7}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by x-3.

$$\left(2x-6\right)\left(y-3\right)+3=x$$

Use the distributive property to multiply 2x-6 by y-3.

$$2xy-6x-6y+18+3=x$$

Add 18 and 3 to get 21.

$$2xy-6x-6y+21=x$$

Subtract x from both sides.

$$2xy-6x-6y+21-x=0$$

Combine -6x and -x to get -7x.

$$2xy-7x-6y+21=0$$

Add 6y to both sides. Anything plus zero gives itself.

$$2xy-7x+21=6y$$

Subtract 21 from both sides.

$$2xy-7x=6y-21$$

Combine all terms containing x.

$$\left(2y-7\right)x=6y-21$$

Divide both sides by -7+2y.

$$\frac{\left(2y-7\right)x}{2y-7}=\frac{6y-21}{2y-7}$$

Dividing by -7+2y undoes the multiplication by -7+2y.

$$x=\frac{6y-21}{2y-7}$$

Divide 6y-21 by -7+2y.

$$x=3$$

Solve for y

$$\left\{\begin{matrix}\\y=\frac{7}{2}\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=3\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by x-3.

$$\left(2x-6\right)\left(y-3\right)+3=x$$

Use the distributive property to multiply 2x-6 by y-3.

$$2xy-6x-6y+18+3=x$$

Add 18 and 3 to get 21.

$$2xy-6x-6y+21=x$$

Add 6x to both sides.

$$2xy-6y+21=x+6x$$

Combine x and 6x to get 7x.

$$2xy-6y+21=7x$$

Subtract 21 from both sides.

$$2xy-6y=7x-21$$

Combine all terms containing y.

$$\left(2x-6\right)y=7x-21$$

Divide both sides by 2x-6.

$$\frac{\left(2x-6\right)y}{2x-6}=\frac{7x-21}{2x-6}$$

Dividing by 2x-6 undoes the multiplication by 2x-6.

$$y=\frac{7x-21}{2x-6}$$

Divide -21+7x by 2x-6.

$$y=\frac{7}{2}$$