Solve (4x+2)*(2y-1)=12

$$( 4 x + 2 ) \times ( 2 y - 1 ) = 12$$

Solve for x

$$x=-\frac{2y-7}{2\left(2y-1\right)}$$

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

Steps for Solving Linear Equation

Use the distributive property to multiply 4x+2 by 2y-1.

$$8xy-4x+4y-2=12$$

Subtract 4y from both sides.

$$8xy-4x-2=12-4y$$

Add 2 to both sides.

$$8xy-4x=12-4y+2$$

Add 12 and 2 to get 14.

$$8xy-4x=14-4y$$

Combine all terms containing x.

$$\left(8y-4\right)x=14-4y$$

Divide both sides by 8y-4.

$$\frac{\left(8y-4\right)x}{8y-4}=\frac{14-4y}{8y-4}$$

Dividing by 8y-4 undoes the multiplication by 8y-4.

$$x=\frac{14-4y}{8y-4}$$

Divide 14-4y by 8y-4.

$$x=\frac{7-2y}{2\left(2y-1\right)}$$

Solve for y

$$y=\frac{2x+7}{2\left(2x+1\right)}$$

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

Steps for Solving Linear Equation

Use the distributive property to multiply 4x+2 by 2y-1.

$$8xy-4x+4y-2=12$$

Add 4x to both sides.

$$8xy+4y-2=12+4x$$

Add 2 to both sides.

$$8xy+4y=12+4x+2$$

Add 12 and 2 to get 14.

$$8xy+4y=14+4x$$

Combine all terms containing y.

$$\left(8x+4\right)y=14+4x$$

The equation is in standard form.

$$\left(8x+4\right)y=4x+14$$

Divide both sides by 8x+4.

$$\frac{\left(8x+4\right)y}{8x+4}=\frac{4x+14}{8x+4}$$

Dividing by 8x+4 undoes the multiplication by 8x+4.

$$y=\frac{4x+14}{8x+4}$$

Divide 14+4x by 8x+4.

$$y=\frac{2x+7}{2\left(2x+1\right)}$$