Solve c=a-c/b

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

Solve for a

$$a=c\left(b+1\right)$$

$$b\neq 0$$

Solution Steps

Multiply both sides of the equation by b.

$$cb=a-c$$

Swap sides so that all variable terms are on the left hand side.

$$a-c=cb$$

Add c to both sides.

$$a=cb+c$$

Solve for b

$$\left\{\begin{matrix}b=\frac{a}{c}-1\text{, }&c\neq a\text{ and }c\neq 0\\b\neq 0\text{, }&c=0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by b.

$$cb=a-c$$

Divide both sides by c.

$$\frac{cb}{c}=\frac{a-c}{c}$$

Dividing by c undoes the multiplication by c.

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

Divide a-c by c.

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

Variable b cannot be equal to 0.

$$b=\frac{a}{c}-1\text{, }b\neq 0$$