Solve for z -8(3/4z-2-1/2z)-12=2z

$- 8 (\frac{3}{4} z - 2 - \frac{1}{2} z) - 12 = 2 z$

Simplify $- 8 (\frac{3}{4} z - 2 - \frac{1}{2} z) - 12$ .

Simplify each term.

Combine $\frac{3}{4}$ and $z$ .

$- 8 (\frac{3 z}{4} - 2 - \frac{1}{2} z) - 12 = 2 z$

Combine $z$ and $\frac{1}{2}$ .

$- 8 (\frac{3 z}{4} - 2 - \frac{z}{2}) - 12 = 2 z$

To write $- \frac{z}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 8 (\frac{3 z}{4} - \frac{z}{2} \cdot \frac{2}{2} - 2) - 12 = 2 z$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{z}{2}$ by $\frac{2}{2}$ .

$- 8 (\frac{3 z}{4} - \frac{z \cdot 2}{2 \cdot 2} - 2) - 12 = 2 z$

Multiply $2$ by $2$ .

$- 8 (\frac{3 z}{4} - \frac{z \cdot 2}{4} - 2) - 12 = 2 z$

Combine the numerators over the common denominator.

$- 8 (\frac{3 z - z \cdot 2}{4} - 2) - 12 = 2 z$

Simplify each term.

Simplify the numerator.

Factor $z$ out of $3 z - z \cdot 2$ .

Factor $z$ out of $3 z$ .

$- 8 (\frac{z \cdot 3 - z \cdot 2}{4} - 2) - 12 = 2 z$

Factor $z$ out of $- z \cdot 2$ .

$- 8 (\frac{z \cdot 3 + z (- 1 \cdot 2)}{4} - 2) - 12 = 2 z$

Factor $z$ out of $z \cdot 3 + z (- 1 \cdot 2)$ .

$- 8 (\frac{z (3 - 1 \cdot 2)}{4} - 2) - 12 = 2 z$

Multiply $- 1$ by $2$ .

$- 8 (\frac{z (3 - 2)}{4} - 2) - 12 = 2 z$

Subtract $2$ from $3$ .

$- 8 (\frac{z \cdot 1}{4} - 2) - 12 = 2 z$

Multiply $z$ by $1$ .

$- 8 (\frac{z}{4} - 2) - 12 = 2 z$

Apply the distributive property.

$- 8 \frac{z}{4} - 8 \cdot - 2 - 12 = 2 z$

Cancel the common factor of $4$ .

Factor $4$ out of $- 8$ .

$4 (- 2) \frac{z}{4} - 8 \cdot - 2 - 12 = 2 z$

Cancel the common factor.

$4 \cdot - 2 \frac{z}{4} - 8 \cdot - 2 - 12 = 2 z$

Rewrite the expression.

$- 2 z - 8 \cdot - 2 - 12 = 2 z$

Multiply $- 8$ by $- 2$ .

$- 2 z + 16 - 12 = 2 z$

Subtract $12$ from $16$ .

$- 2 z + 4 = 2 z$

Move all terms containing $z$ to the left side of the equation.

Subtract $2 z$ from both sides of the equation.

$- 2 z + 4 - 2 z = 0$

Subtract $2 z$ from $- 2 z$ .

$- 4 z + 4 = 0$

Subtract $4$ from both sides of the equation.

$- 4 z = - 4$

Divide each term in $- 4 z = - 4$ by $- 4$ and simplify.

Divide each term in $- 4 z = - 4$ by $- 4$ .

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

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

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

Divide $z$ by $1$ .

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

Simplify the right side.

Divide $- 4$ by $- 4$ .

$z = 1$

Solve for z -8(3/4z-2-1/2z)-12=2z

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