Solve yz+4=2yz+6y

$$yz+4=2yz+6y$$

Solve for y

$$y=\frac{4}{z+6}$$

$$z\neq -6$$

Steps for Solving Linear Equation

Subtract 2yz from both sides.

$$yz+4-2yz=6y$$

Combine yz and -2yz to get -yz.

$$-yz+4=6y$$

Subtract 6y from both sides.

$$-yz+4-6y=0$$

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$-yz-6y=-4$$

Combine all terms containing y.

$$\left(-z-6\right)y=-4$$

Divide both sides by -z-6.

$$\frac{\left(-z-6\right)y}{-z-6}=-\frac{4}{-z-6}$$

Dividing by -z-6 undoes the multiplication by -z-6.

$$y=-\frac{4}{-z-6}$$

Divide -4 by -z-6.

$$y=\frac{4}{z+6}$$

Solve for z

$$z=-6+\frac{4}{y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Subtract 2yz from both sides.

$$yz+4-2yz=6y$$

Combine yz and -2yz to get -yz.

$$-yz+4=6y$$

Subtract 4 from both sides.

$$-yz=6y-4$$

The equation is in standard form.

$$\left(-y\right)z=6y-4$$

Divide both sides by -y.

$$\frac{\left(-y\right)z}{-y}=\frac{6y-4}{-y}$$

Dividing by -y undoes the multiplication by -y.

$$z=\frac{6y-4}{-y}$$

Divide -4+6y by -y.

$$z=-6+\frac{4}{y}$$