Solve for d a=b-cd

$a = b - c d$

Rewrite the equation as $b - c d = a$ .

$b - c d = a$

Subtract $b$ from both sides of the equation.

$- c d = a - b$

Divide each term in $- c d = a - b$ by $- 1 c$ and simplify.

Divide each term in $- c d = a - b$ by $- 1 c$ .

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Cancel the common factor of $c$ .

Cancel the common factor.

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

Divide $d$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Dividing two negative values results in a positive value.

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