Solve for z w=p(y-z)

$w = p (y - z)$

Step 1

Rewrite the equation as $p (y - z) = w$ .

$p (y - z) = w$

Step 2

Divide each term in $p (y - z) = w$ by $p$ and simplify.

Divide each term in $p (y - z) = w$ by $p$ .

$\frac{p (y - z)}{p} = \frac{w}{p}$

Simplify the left side.

Cancel the common factor of $p$ .

Cancel the common factor.

$\frac{p (y - z)}{p} = \frac{w}{p}$

Divide $y - z$ by $1$ .

$y - z = \frac{w}{p}$

Step 3

Subtract $y$ from both sides of the equation.

$- z = \frac{w}{p} - y$

Step 4

Divide each term in $- z = \frac{w}{p} - y$ by $- 1$ and simplify.

Divide each term in $- z = \frac{w}{p} - y$ by $- 1$ .

$\frac{- z}{- 1} = \frac{\frac{w}{p}}{- 1} + \frac{- y}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{z}{1} = \frac{\frac{w}{p}}{- 1} + \frac{- y}{- 1}$

Divide $z$ by $1$ .

$z = \frac{\frac{w}{p}}{- 1} + \frac{- y}{- 1}$

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{\frac{w}{p}}{- 1}$ .

$z = - 1 \cdot \frac{w}{p} + \frac{- y}{- 1}$

Rewrite $- 1 \cdot \frac{w}{p}$ as $- \frac{w}{p}$ .

$z = - \frac{w}{p} + \frac{- y}{- 1}$

Dividing two negative values results in a positive value.

$z = - \frac{w}{p} + \frac{y}{1}$

Divide $y$ by $1$ .

$z = - \frac{w}{p} + y$