Solve for n 5z=7n+8nz

$5 z = 7 n + 8 n z$

Rewrite the equation as $7 n + 8 n z = 5 z$ .

$7 n + 8 n z = 5 z$

Factor $n$ out of $7 n + 8 n z$ .

Factor $n$ out of $7 n$ .

$n \cdot 7 + 8 n z = 5 z$

Factor $n$ out of $8 n z$ .

$n \cdot 7 + n (8 z) = 5 z$

Factor $n$ out of $n \cdot 7 + n (8 z)$ .

$n (7 + 8 z) = 5 z$

Divide each term in $n (7 + 8 z) = 5 z$ by $7 + 8 z$ and simplify.

Divide each term in $n (7 + 8 z) = 5 z$ by $7 + 8 z$ .

$\frac{n (7 + 8 z)}{7 + 8 z} = \frac{5 z}{7 + 8 z}$

Simplify the left side.

Cancel the common factor of $7 + 8 z$ .

Cancel the common factor.

$\frac{n (7 + 8 z)}{7 + 8 z} = \frac{5 z}{7 + 8 z}$

Divide $n$ by $1$ .

$n = \frac{5 z}{7 + 8 z}$