Solve for z 12=(2+z)/-6

$12 = \frac{2 + z}{- 6}$

Step 1

Rewrite the equation as $\frac{2 + z}{- 6} = 12$ .

$\frac{2 + z}{- 6} = 12$

Step 2

Multiply both sides of the equation by $- 6$ .

$- 6 \frac{2 + z}{- 6} = - 6 \cdot 12$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 6 \frac{2 + z}{- 6}$ .

Cancel the common factor of $6$ .

Factor $6$ out of $- 6$ .

$6 (- 1) \frac{2 + z}{- 6} = - 6 \cdot 12$

Factor $6$ out of $- 6$ .

$6 \cdot - 1 \frac{2 + z}{6 \cdot - 1} = - 6 \cdot 12$

Cancel the common factor.

$6 \cdot - 1 \frac{2 + z}{6 \cdot - 1} = - 6 \cdot 12$

Rewrite the expression.

$- \frac{2 + z}{- 1} = - 6 \cdot 12$

Simplify the expression.

Move the negative one from the denominator of $\frac{2 + z}{- 1}$ .

$- (- 1 \cdot (2 + z)) = - 6 \cdot 12$

Rewrite $- 1 \cdot (2 + z)$ as $- (2 + z)$ .

$- - (2 + z) = - 6 \cdot 12$

Apply the distributive property.

$- (- 1 \cdot 2 - z) = - 6 \cdot 12$

Multiply $- 1$ by $2$ .

$- (- 2 - z) = - 6 \cdot 12$

Apply the distributive property.

$- - 2 - - z = - 6 \cdot 12$

Multiply $- 1$ by $- 2$ .

$2 - - z = - 6 \cdot 12$

Multiply $- - z$ .

Multiply $- 1$ by $- 1$ .

$2 + 1 z = - 6 \cdot 12$

Multiply $z$ by $1$ .

$2 + z = - 6 \cdot 12$

Simplify the right side.

Multiply $- 6$ by $12$ .

$2 + z = - 72$

Step 4

Move all terms not containing $z$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$z = - 72 - 2$

Subtract $2$ from $- 72$ .

$z = - 74$

Solve for z 12=(2+z)/-6

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