Solve for c a=b+bcd

$a = b + b c d$

Step 1

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

$b + b c d = a$

Step 2

Subtract $b$ from both sides of the equation.

$b c d = a - b$

Step 3

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

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

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

Simplify the left side.

Cancel the common factor of $b$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $d$ .

Cancel the common factor.

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

Divide $c$ by $1$ .

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $b$ .

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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