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

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

Solve for x

$$x=\frac{y+3}{2\left(y+2\right)}$$

$$y\neq -2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x-1 by y+3.

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

Subtract 2x from both sides.

$$2xy+6x-y-3-2x=0$$

Combine 6x and -2x to get 4x.

$$2xy+4x-y-3=0$$

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

$$2xy+4x-3=y$$

Add 3 to both sides.

$$2xy+4x=y+3$$

Combine all terms containing x.

$$\left(2y+4\right)x=y+3$$

Divide both sides by 2y+4.

$$\frac{\left(2y+4\right)x}{2y+4}=\frac{y+3}{2y+4}$$

Dividing by 2y+4 undoes the multiplication by 2y+4.

$$x=\frac{y+3}{2y+4}$$

Divide y+3 by 2y+4.

$$x=\frac{y+3}{2\left(y+2\right)}$$

Solve for y

$$y=-\frac{4x-3}{2x-1}$$

$$x\neq \frac{1}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x-1 by y+3.

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

Subtract 6x from both sides.

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

Combine 2x and -6x to get -4x.

$$2xy-y-3=-4x$$

Add 3 to both sides.

$$2xy-y=-4x+3$$

Combine all terms containing y.

$$\left(2x-1\right)y=-4x+3$$

The equation is in standard form.

$$\left(2x-1\right)y=3-4x$$

Divide both sides by 2x-1.

$$\frac{\left(2x-1\right)y}{2x-1}=\frac{3-4x}{2x-1}$$

Dividing by 2x-1 undoes the multiplication by 2x-1.

$$y=\frac{3-4x}{2x-1}$$