Algebra Examples

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

Step 1

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

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Step 1.1

Rewrite.

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

Step 1.2

Simplify by adding zeros.

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

Step 1.3

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 $- p z + 2 z$ .

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Step 4.1

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

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

Step 4.2

Factor $z$ out of $2 z$ .

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

Step 4.3

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.

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Step 5.1

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

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

Step 5.2

Simplify the left side.

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Step 5.2.1

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

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Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $z$ by $1$ .

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

Step 5.3

Simplify the right side.

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Step 5.3.1

Combine the numerators over the common denominator.

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

Step 5.3.2

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

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

Step 5.3.3

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

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

Step 5.3.4

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

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

Step 5.3.5

Rewrite negatives.

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Step 5.3.5.1

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

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

Step 5.3.5.2

Move the negative in front of the fraction.

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