Solve for x d(x+a)=c(x+b)

$d (x + a) = c (x + b)$

Step 1

Simplify $d (x + a)$ .

Start simplifying.

$0 + 0 + d (x + a) = c (x + b)$

Simplify by adding zeros.

$d (x + a) = c (x + b)$

Apply the distributive property.

$d x + d a = c (x + b)$

Step 2

Apply the distributive property.

$d x + d a = c x + c b$

Step 3

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

$d x + d a - c x = c b$

Step 4

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

$d x - c x = c b - d a$

Step 5

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

Factor $x$ out of $d x$ .

$x d - c x = c b - d a$

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

$x d + x (- c) = c b - d a$

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

$x (d - c) = c b - d a$

Step 6

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

Divide each term in $x (d - c) = c b - d a$ by $d - c$ .

$\frac{x (d - c)}{d - c} = \frac{c b}{d - c} + \frac{- d a}{d - c}$

Simplify the left side.

Cancel the common factor of $d - c$ .

Cancel the common factor.

$\frac{x (d - c)}{d - c} = \frac{c b}{d - c} + \frac{- d a}{d - c}$

Divide $x$ by $1$ .

$x = \frac{c b}{d - c} + \frac{- d a}{d - c}$

Simplify the right side.

Combine the numerators over the common denominator.

$x = \frac{c b - d a}{d - c}$