Solve for y cx-d=a(x-y)

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

Rewrite the equation as $a (x - y) = c x - d$ .

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

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

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

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

Simplify the left side.

Cancel the common factor of $a$ .

Cancel the common factor.

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

Divide $x - y$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Subtract $x$ from both sides of the equation.

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

Divide each term in $- y = \frac{c x}{a} - \frac{d}{a} - x$ by $- 1$ and simplify.

Divide each term in $- y = \frac{c x}{a} - \frac{d}{a} - x$ by $- 1$ .

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{\frac{c x}{a}}{- 1}$ .

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

Rewrite $- 1 \cdot \frac{c x}{a}$ as $- \frac{c x}{a}$ .

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

Dividing two negative values results in a positive value.

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

Divide $\frac{d}{a}$ by $1$ .

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

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

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