Solve -6=a(z+1)*(2-4)

$$- 6 = a ( z + 1 ) \cdot ( 2 - 4 )$$

Solve for a

$$a=\frac{3}{z+1}$$

$$z\neq -1$$

Steps for Solving Linear Equation

Subtract 4 from 2 to get -2.

$$-6=a\left(z+1\right)\left(-2\right)$$

Use the distributive property to multiply a by z+1.

$$-6=\left(az+a\right)\left(-2\right)$$

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

$$-6=-2az-2a$$

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

$$-2az-2a=-6$$

Combine all terms containing a.

$$\left(-2z-2\right)a=-6$$

Divide both sides by -2z-2.

$$\frac{\left(-2z-2\right)a}{-2z-2}=-\frac{6}{-2z-2}$$

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

$$a=-\frac{6}{-2z-2}$$

Divide -6 by -2z-2.

$$a=\frac{3}{z+1}$$

Solve for z

$$z=-1+\frac{3}{a}$$

$$a\neq 0$$

Steps for Solving Linear Equation

Subtract 4 from 2 to get -2.

$$-6=a\left(z+1\right)\left(-2\right)$$

Use the distributive property to multiply a by z+1.

$$-6=\left(az+a\right)\left(-2\right)$$

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

$$-6=-2az-2a$$

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

$$-2az-2a=-6$$

Add 2a to both sides.

$$-2az=-6+2a$$

The equation is in standard form.

$$\left(-2a\right)z=2a-6$$

Divide both sides by -2a.

$$\frac{\left(-2a\right)z}{-2a}=\frac{2a-6}{-2a}$$

Dividing by -2a undoes the multiplication by -2a.

$$z=\frac{2a-6}{-2a}$$

Divide -6+2a by -2a.

$$z=-1+\frac{3}{a}$$