Solve for r s=l(1-r)

$s = l (1 - r)$

Step 1

Rewrite the equation as $l (1 - r) = s$ .

$l (1 - r) = s$

Step 2

Divide each term in $l (1 - r) = s$ by $l$ and simplify.

Divide each term in $l (1 - r) = s$ by $l$ .

$\frac{l (1 - r)}{l} = \frac{s}{l}$

Simplify the left side.

Cancel the common factor of $l$ .

Cancel the common factor.

$\frac{l (1 - r)}{l} = \frac{s}{l}$

Divide $1 - r$ by $1$ .

$1 - r = \frac{s}{l}$

Step 3

Subtract $1$ from both sides of the equation.

$- r = \frac{s}{l} - 1$

Step 4

Divide each term in $- r = \frac{s}{l} - 1$ by $- 1$ and simplify.

Divide each term in $- r = \frac{s}{l} - 1$ by $- 1$ .

$\frac{- r}{- 1} = \frac{\frac{s}{l}}{- 1} + \frac{- 1}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{r}{1} = \frac{\frac{s}{l}}{- 1} + \frac{- 1}{- 1}$

Divide $r$ by $1$ .

$r = \frac{\frac{s}{l}}{- 1} + \frac{- 1}{- 1}$

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{\frac{s}{l}}{- 1}$ .

$r = - 1 \cdot \frac{s}{l} + \frac{- 1}{- 1}$

Rewrite $- 1 \cdot \frac{s}{l}$ as $- \frac{s}{l}$ .

$r = - \frac{s}{l} + \frac{- 1}{- 1}$

Divide $- 1$ by $- 1$ .

$r = - \frac{s}{l} + 1$