Solve z=3a+2/-2a+3

$$z = \frac { 3 a + 2 } { - 2 a + 3 }$$

Solve for a

$$a=\frac{3z-2}{2z+3}$$

$$z\neq -\frac{3}{2}$$

Steps for Solving Linear Equation

Variable a cannot be equal to \frac{3}{2} since division by zero is not defined. Multiply both sides of the equation by -2a+3.

$$z\left(-2a+3\right)=3a+2$$

Use the distributive property to multiply z by -2a+3.

$$-2za+3z=3a+2$$

Subtract 3a from both sides.

$$-2za+3z-3a=2$$

Subtract 3z from both sides.

$$-2za-3a=2-3z$$

Combine all terms containing a.

$$\left(-2z-3\right)a=2-3z$$

Divide both sides by -2z-3.

$$\frac{\left(-2z-3\right)a}{-2z-3}=\frac{2-3z}{-2z-3}$$

Dividing by -2z-3 undoes the multiplication by -2z-3.

$$a=\frac{2-3z}{-2z-3}$$

Divide 2-3z by -2z-3.

$$a=-\frac{2-3z}{2z+3}$$

Variable a cannot be equal to \frac{3}{2}.

$$a=-\frac{2-3z}{2z+3}\text{, }a\neq \frac{3}{2}$$

Solve for z

$$z=\frac{3a+2}{3-2a}$$

$$a\neq \frac{3}{2}$$