Solve for x y(x+w)=c(x+z)

$y (x + w) = c (x + z)$

Step 1

Simplify $y (x + w)$ .

Rewrite.

$0 + 0 + y (x + w) = c (x + z)$

Simplify by adding zeros.

$y (x + w) = c (x + z)$

Apply the distributive property.

$y x + y w = c (x + z)$

Step 2

Apply the distributive property.

$y x + y w = c x + c z$

Step 3

Subtract $c x$ from both sides of the equation.

$y x + y w - c x = c z$

Step 4

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

$y x - c x = c z - y w$

Step 5

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

Factor $x$ out of $y x$ .

$x y - c x = c z - y w$

Factor $x$ out of $- c x$ .

$x y + x (- c) = c z - y w$

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

$x (y - c) = c z - y w$

Step 6

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

Divide each term in $x (y - c) = c z - y w$ by $y - c$ .

$\frac{x (y - c)}{y - c} = \frac{c z}{y - c} + \frac{- y w}{y - c}$

Simplify the left side.

Cancel the common factor of $y - c$ .

Cancel the common factor.

$\frac{x (y - c)}{y - c} = \frac{c z}{y - c} + \frac{- y w}{y - c}$

Divide $x$ by $1$ .

$x = \frac{c z}{y - c} + \frac{- y w}{y - c}$

Simplify the right side.

Combine the numerators over the common denominator.

$x = \frac{c z - y w}{y - c}$