Solve for z -p*(d+z)=-2z+59

$- p \cdot (d + z) = - 2 z + 59$

Step 1

Simplify $- p \cdot (d + z)$ .

Rewrite.

$0 + 0 - p \cdot (d + z) = - 2 z + 59$

Simplify by adding zeros.

$- p \cdot (d + z) = - 2 z + 59$

Apply the distributive property.

$- p d - p z = - 2 z + 59$

Step 2

Add $2 z$ to both sides of the equation.

$- p d - p z + 2 z = 59$

Step 3

Add $p d$ to both sides of the equation.

$- p z + 2 z = 59 + p d$

Step 4

Factor $z$ out of $- p z + 2 z$ .

Factor $z$ out of $- p z$ .

$z (- p) + 2 z = 59 + p d$

Factor $z$ out of $2 z$ .

$z (- p) + z \cdot 2 = 59 + p d$

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

$z (- p + 2) = 59 + p d$

Step 5

Divide each term in $z (- p + 2) = 59 + p d$ by $- p + 2$ and simplify.

Divide each term in $z (- p + 2) = 59 + p d$ by $- p + 2$ .

$\frac{z (- p + 2)}{- p + 2} = \frac{59}{- p + 2} + \frac{p d}{- p + 2}$

Simplify the left side.

Cancel the common factor of $- p + 2$ .

Cancel the common factor.

$\frac{z (- p + 2)}{- p + 2} = \frac{59}{- p + 2} + \frac{p d}{- p + 2}$

Divide $z$ by $1$ .

$z = \frac{59}{- p + 2} + \frac{p d}{- p + 2}$

Simplify the right side.

Combine the numerators over the common denominator.

$z = \frac{59 + p d}{- p + 2}$

Factor $- 1$ out of $- p$ .

$z = \frac{59 + p d}{- (p) + 2}$

Rewrite $2$ as $- 1 (- 2)$ .

$z = \frac{59 + p d}{- (p) - 1 (- 2)}$

Factor $- 1$ out of $- (p) - 1 (- 2)$ .

$z = \frac{59 + p d}{- (p - 2)}$

Rewrite negatives.

Rewrite $- (p - 2)$ as $- 1 (p - 2)$ .

$z = \frac{59 + p d}{- 1 (p - 2)}$

Move the negative in front of the fraction.

$z = - \frac{59 + p d}{p - 2}$

Solve for z -p*(d+z)=-2z+59

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