Solve 8y=-2y*3z+4=

$$8 y = - 2 y \cdot 3 z + 4 =$$

Solve for y

$$y=\frac{2}{3z+4}$$

$$z\neq -\frac{4}{3}$$

Steps for Solving Linear Equation

Multiply -2 and 3 to get -6.

$$8y=-6yz+4$$

Add 6yz to both sides.

$$8y+6yz=4$$

Combine all terms containing y.

$$\left(8+6z\right)y=4$$

The equation is in standard form.

$$\left(6z+8\right)y=4$$

Divide both sides by 6z+8.

$$\frac{\left(6z+8\right)y}{6z+8}=\frac{4}{6z+8}$$

Dividing by 6z+8 undoes the multiplication by 6z+8.

$$y=\frac{4}{6z+8}$$

Divide 4 by 6z+8.

$$y=\frac{2}{3z+4}$$

Solve for z

$$z=-\frac{4}{3}+\frac{2}{3y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply -2 and 3 to get -6.

$$8y=-6yz+4$$

Swap sides so that all variable terms are on the left hand side.

$$-6yz+4=8y$$

Subtract 4 from both sides.

$$-6yz=8y-4$$

The equation is in standard form.

$$\left(-6y\right)z=8y-4$$

Divide both sides by -6y.

$$\frac{\left(-6y\right)z}{-6y}=\frac{8y-4}{-6y}$$

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

$$z=\frac{8y-4}{-6y}$$

Divide 8y-4 by -6y.

$$z=-\frac{4}{3}+\frac{2}{3y}$$