Solve 2xy-4x+6y-3=0

$$2 x y - 4 x + 6 y - 3 = 0$$

Solve for x

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

$$y\neq 2$$

Steps for Solving Linear Equation

Subtract 6y from both sides. Anything subtracted from zero gives its negation.

$$2xy-4x-3=-6y$$

Add 3 to both sides.

$$2xy-4x=-6y+3$$

Combine all terms containing x.

$$\left(2y-4\right)x=-6y+3$$

The equation is in standard form.

$$\left(2y-4\right)x=3-6y$$

Divide both sides by 2y-4.

$$\frac{\left(2y-4\right)x}{2y-4}=\frac{3-6y}{2y-4}$$

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

$$x=\frac{3-6y}{2y-4}$$

Divide -6y+3 by 2y-4.

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

Solve for y

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

$$x\neq -3$$

Steps for Solving Linear Equation

Add 4x to both sides. Anything plus zero gives itself.

$$2xy+6y-3=4x$$

Add 3 to both sides.

$$2xy+6y=4x+3$$

Combine all terms containing y.

$$\left(2x+6\right)y=4x+3$$

Divide both sides by 2x+6.

$$\frac{\left(2x+6\right)y}{2x+6}=\frac{4x+3}{2x+6}$$

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

$$y=\frac{4x+3}{2x+6}$$

Divide 4x+3 by 2x+6.

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