Solve (x-3)(2y+1)=7

$$( x - 3 ) ( 2 y + 1 ) = 7$$

Solve for x

$$x=\frac{2\left(3y+5\right)}{2y+1}$$

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

Steps for Solving Linear Equation

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

$$2xy+x-6y-3=7$$

Add 6y to both sides.

$$2xy+x-3=7+6y$$

Add 3 to both sides.

$$2xy+x=7+6y+3$$

Add 7 and 3 to get 10.

$$2xy+x=10+6y$$

Combine all terms containing x.

$$\left(2y+1\right)x=10+6y$$

The equation is in standard form.

$$\left(2y+1\right)x=6y+10$$

Divide both sides by 2y+1.

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

Dividing by 2y+1 undoes the multiplication by 2y+1.

$$x=\frac{6y+10}{2y+1}$$

Divide 10+6y by 2y+1.

$$x=\frac{2\left(3y+5\right)}{2y+1}$$

Solve for y

$$y=-\frac{x-10}{2\left(x-3\right)}$$

$$x\neq 3$$

Steps for Solving Linear Equation

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

$$2xy+x-6y-3=7$$

Subtract x from both sides.

$$2xy-6y-3=7-x$$

Add 3 to both sides.

$$2xy-6y=7-x+3$$

Add 7 and 3 to get 10.

$$2xy-6y=10-x$$

Combine all terms containing y.

$$\left(2x-6\right)y=10-x$$

Divide both sides by 2x-6.

$$\frac{\left(2x-6\right)y}{2x-6}=\frac{10-x}{2x-6}$$

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

$$y=\frac{10-x}{2x-6}$$

Divide 10-x by 2x-6.

$$y=\frac{10-x}{2\left(x-3\right)}$$