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

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

Step 1

Apply the distributive property.

$a x + a b - c = d$

Step 2

Move all terms not containing $x$ to the right side of the equation.

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

$a x - c = d - a b$

Add $c$ to both sides of the equation.

$a x = d - a b + c$

Step 3

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

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

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

Simplify the left side.

Cancel the common factor of $a$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $a$ .

Cancel the common factor.

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

Divide $- 1 b$ by $1$ .

$x = \frac{d}{a} - 1 b + \frac{c}{a}$

Rewrite $- 1 b$ as $- b$ .

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