Solve for d ab-cd=e

$a b - c d = e$

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

$- c d = e - a b$

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

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

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Cancel the common factor of $c$ .

Cancel the common factor.

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

Divide $d$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Dividing two negative values results in a positive value.

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