Solve 2x-2-3x(y-4)=0

$$2 x - 2 - 3 x ( y - 4 ) = 0$$

Solve for x

$$x=\frac{2}{14-3y}$$

$$y\neq \frac{14}{3}$$

Steps for Solving Linear Equation

Multiply -1 and 3 to get -3.

$$2x-2-3x\left(y-4\right)=0$$

Use the distributive property to multiply -3x by y-4.

$$2x-2-3xy+12x=0$$

Combine 2x and 12x to get 14x.

$$14x-2-3xy=0$$

Add 2 to both sides. Anything plus zero gives itself.

$$14x-3xy=2$$

Combine all terms containing x.

$$\left(14-3y\right)x=2$$

Divide both sides by -3y+14.

$$\frac{\left(14-3y\right)x}{14-3y}=\frac{2}{14-3y}$$

Dividing by -3y+14 undoes the multiplication by -3y+14.

$$x=\frac{2}{14-3y}$$

Solve for y

$$y=\frac{14}{3}-\frac{2}{3x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply -1 and 3 to get -3.

$$2x-2-3x\left(y-4\right)=0$$

Use the distributive property to multiply -3x by y-4.

$$2x-2-3xy+12x=0$$

Combine 2x and 12x to get 14x.

$$14x-2-3xy=0$$

Subtract 14x from both sides. Anything subtracted from zero gives its negation.

$$-2-3xy=-14x$$

Add 2 to both sides.

$$-3xy=-14x+2$$

The equation is in standard form.

$$\left(-3x\right)y=2-14x$$

Divide both sides by -3x.

$$\frac{\left(-3x\right)y}{-3x}=\frac{2-14x}{-3x}$$

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

$$y=\frac{2-14x}{-3x}$$

Divide -14x+2 by -3x.

$$y=\frac{14}{3}-\frac{2}{3x}$$