Solve (2x-1)*(-3y+1)=6

$$( 2 x - 1 ) \cdot ( - 3 y + 1 ) = 6$$

Solve for x

$$x=-\frac{3y-7}{2\left(1-3y\right)}$$

$$y\neq \frac{1}{3}$$

Steps for Solving Linear Equation

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

$$-6xy+2x+3y-1=6$$

Subtract 3y from both sides.

$$-6xy+2x-1=6-3y$$

Add 1 to both sides.

$$-6xy+2x=6-3y+1$$

Add 6 and 1 to get 7.

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

Combine all terms containing x.

$$\left(-6y+2\right)x=7-3y$$

The equation is in standard form.

$$\left(2-6y\right)x=7-3y$$

Divide both sides by -6y+2.

$$\frac{\left(2-6y\right)x}{2-6y}=\frac{7-3y}{2-6y}$$

Dividing by -6y+2 undoes the multiplication by -6y+2.

$$x=\frac{7-3y}{2-6y}$$

Divide 7-3y by -6y+2.

$$x=\frac{7-3y}{2\left(1-3y\right)}$$

Solve for y

$$y=-\frac{2x-7}{3\left(1-2x\right)}$$

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

Steps for Solving Linear Equation

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

$$-6xy+2x+3y-1=6$$

Subtract 2x from both sides.

$$-6xy+3y-1=6-2x$$

Add 1 to both sides.

$$-6xy+3y=6-2x+1$$

Add 6 and 1 to get 7.

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

Combine all terms containing y.

$$\left(-6x+3\right)y=7-2x$$

The equation is in standard form.

$$\left(3-6x\right)y=7-2x$$

Divide both sides by -6x+3.

$$\frac{\left(3-6x\right)y}{3-6x}=\frac{7-2x}{3-6x}$$

Dividing by -6x+3 undoes the multiplication by -6x+3.

$$y=\frac{7-2x}{3-6x}$$

Divide 7-2x by -6x+3.

$$y=\frac{7-2x}{3\left(1-2x\right)}$$