Solve for z w*(-4+z)=mz+17

$w \cdot (- 4 + z) = m z + 17$

Simplify $w \cdot (- 4 + z)$ .

Rewrite.

$0 + 0 + w \cdot (- 4 + z) = m z + 17$

Simplify by adding zeros.

$w \cdot (- 4 + z) = m z + 17$

Apply the distributive property.

$w \cdot - 4 + w z = m z + 17$

Move $- 4$ to the left of $w$ .

$- 4 w + w z = m z + 17$

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

$- 4 w + w z - m z = 17$

Add $4 w$ to both sides of the equation.

$w z - m z = 17 + 4 w$

Factor $z$ out of $w z - m z$ .

Factor $z$ out of $w z$ .

$z w - m z = 17 + 4 w$

Factor $z$ out of $- m z$ .

$z w + z (- m) = 17 + 4 w$

Factor $z$ out of $z w + z (- m)$ .

$z (w - m) = 17 + 4 w$

Divide each term in $z (w - m) = 17 + 4 w$ by $w - m$ and simplify.

Divide each term in $z (w - m) = 17 + 4 w$ by $w - m$ .

$\frac{z (w - m)}{w - m} = \frac{17}{w - m} + \frac{4 w}{w - m}$

Simplify the left side.

Cancel the common factor of $w - m$ .

Cancel the common factor.

$\frac{z (w - m)}{w - m} = \frac{17}{w - m} + \frac{4 w}{w - m}$

Divide $z$ by $1$ .

$z = \frac{17}{w - m} + \frac{4 w}{w - m}$

Simplify the right side.

Combine the numerators over the common denominator.

$z = \frac{17 + 4 w}{w - m}$