Solve for r S(1-r)=a-b*r

$S (1 - r) = a - b \cdot r$

Simplify $S (1 - r)$ .

Rewrite.

$0 + 0 + S (1 - r) = a - b \cdot r$

Simplify by adding zeros.

$S (1 - r) = a - b \cdot r$

Apply the distributive property.

$S \cdot 1 + S (- r) = a - b \cdot r$

Simplify the expression.

Multiply $S$ by $1$ .

$S + S (- r) = a - b \cdot r$

Rewrite using the commutative property of multiplication.

$S - S r = a - b \cdot r$

$S - S r = a - b r$

Add $b r$ to both sides of the equation.

$S - S r + b r = a$

Subtract $S$ from both sides of the equation.

$- S r + b r = a - S$

Factor $r$ out of $- S r + b r$ .

Factor $r$ out of $- S r$ .

$r (- S) + b r = a - S$

Factor $r$ out of $b r$ .

$r (- S) + r b = a - S$

Factor $r$ out of $r (- S) + r b$ .

$r (- S + b) = a - S$

Divide each term in $r (- S + b) = a - S$ by $- S + b$ and simplify.

Divide each term in $r (- S + b) = a - S$ by $- S + b$ .

$\frac{r (- S + b)}{- S + b} = \frac{a}{- S + b} + \frac{- S}{- S + b}$

Simplify the left side.

Cancel the common factor of $- S + b$ .

Cancel the common factor.

$\frac{r (- S + b)}{- S + b} = \frac{a}{- S + b} + \frac{- S}{- S + b}$

Divide $r$ by $1$ .

$r = \frac{a}{- S + b} + \frac{- S}{- S + b}$

Simplify the right side.

Combine the numerators over the common denominator.

$r = \frac{a - S}{- S + b}$

Factor $- 1$ out of $- S$ .

$r = \frac{a - S}{- (S) + b}$

Factor $- 1$ out of $b$ .

$r = \frac{a - S}{- (S) - 1 (- b)}$

Factor $- 1$ out of $- (S) - 1 (- b)$ .

$r = \frac{a - S}{- (S - b)}$

Rewrite negatives.

Rewrite $- (S - b)$ as $- 1 (S - b)$ .

$r = \frac{a - S}{- 1 (S - b)}$

Move the negative in front of the fraction.

$r = - \frac{a - S}{S - b}$

Solve for r S(1-r)=a-b*r

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