Solve for y a(n+y)=10y+32

$a (n + y) = 10 y + 32$

Simplify $a (n + y)$ .

Rewrite.

$0 + 0 + a (n + y) = 10 y + 32$

Simplify by adding zeros.

$a (n + y) = 10 y + 32$

Apply the distributive property.

$a n + a y = 10 y + 32$

Subtract $10 y$ from both sides of the equation.

$a n + a y - 10 y = 32$

Subtract $a n$ from both sides of the equation.

$a y - 10 y = 32 - a n$

Factor $y$ out of $a y - 10 y$ .

Factor $y$ out of $a y$ .

$y a - 10 y = 32 - a n$

Factor $y$ out of $- 10 y$ .

$y a + y \cdot - 10 = 32 - a n$

Factor $y$ out of $y a + y \cdot - 10$ .

$y (a - 10) = 32 - a n$

Divide each term in $y (a - 10) = 32 - a n$ by $a - 10$ and simplify.

Divide each term in $y (a - 10) = 32 - a n$ by $a - 10$ .

$\frac{y (a - 10)}{a - 10} = \frac{32}{a - 10} + \frac{- a n}{a - 10}$

Simplify the left side.

Cancel the common factor of $a - 10$ .

Cancel the common factor.

$\frac{y (a - 10)}{a - 10} = \frac{32}{a - 10} + \frac{- a n}{a - 10}$

Divide $y$ by $1$ .

$y = \frac{32}{a - 10} + \frac{- a n}{a - 10}$

Simplify the right side.

Combine the numerators over the common denominator.

$y = \frac{32 - a n}{a - 10}$