Solve for x a(x+z)-yx=b

$a (x + z) - y x = b$

Step 1

Apply the distributive property.

$a x + a z - y x = b$

Step 2

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

$a x - y x = b - a z$

Step 3

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

Factor $x$ out of $a x$ .

$x a - y x = b - a z$

Factor $x$ out of $- y x$ .

$x a + x (- y) = b - a z$

Factor $x$ out of $x a + x (- y)$ .

$x (a - y) = b - a z$

Step 4

Divide each term in $x (a - y) = b - a z$ by $a - y$ and simplify.

Divide each term in $x (a - y) = b - a z$ by $a - y$ .

$\frac{x (a - y)}{a - y} = \frac{b}{a - y} + \frac{- a z}{a - y}$

Simplify the left side.

Cancel the common factor of $a - y$ .

Cancel the common factor.

$\frac{x (a - y)}{a - y} = \frac{b}{a - y} + \frac{- a z}{a - y}$

Divide $x$ by $1$ .

$x = \frac{b}{a - y} + \frac{- a z}{a - y}$

Simplify the right side.

Combine the numerators over the common denominator.

$x = \frac{b - a z}{a - y}$