How to solve for z in this equation: - p ( 51 + z ) = d z + 84 ?

Question

How to solve for z in this equation:        -    p          (      51      +      z      )        =          d      z        +    84  ?

Jaime Lutz · Accepted Answer

First, multiply each term inside a parenthesis by the term outside a parenthesis to expand the terms in parenthesis on the left side of the equation:

- p (51 + z) = d z + 84

(- p \times 51) + (- p \times z) = d z + 84

- 51 p + (- p z) = d z + 84

- 51 p - p z = d z + 84

Next add 51p and subtract dz from each side of the equation to isolate the z terms while keeping the equation balanced:

51 p + - 51 p - d z - p z = 51 p - d z + d z + 84

0 - d z - p z = 51 p - 0 + 84

- d z - p z = 51 p + 84

Then, factor a z out of each term on the left side of the equation to give:

(- d - p) z = 51 p + 84

Now, divide each side of the equation by

(- d - p)

to solve for z while keeping the equation balanced:

\frac{(- d - p) z}{(- d - p)} = \frac{51 p + 84}{(- d - p)}

\frac{(- d - p) z}{(- d - p)} = \frac{51 p + 84}{- d - p}

z = \frac{51 p + 84}{- d - p}

How to solve for z in this equation: -p(51+z)=dz+84?