Solve c/a-5x-5c/a-5=c

$$\frac { c } { a - 5 } x - \frac { 5 c } { a - 5 } = c$$

Solve for c (complex solution)

$$\left\{\begin{matrix}c=0\text{, }&a\neq 5\\c\in \mathrm{C}\text{, }&a=x\text{ and }x\neq 5\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a-5.

$$cx-5c=c\left(a-5\right)$$

Use the distributive property to multiply c by a-5.

$$cx-5c=ca-5c$$

Subtract ca from both sides.

$$cx-5c-ca=-5c$$

Add 5c to both sides.

$$cx-5c-ca+5c=0$$

Combine -5c and 5c to get 0.

$$cx-ca=0$$

Combine all terms containing c.

$$\left(x-a\right)c=0$$

Divide 0 by x-a.

$$c=0$$

Solve for a

$$\left\{\begin{matrix}a=x\text{, }&x\neq 5\\a\neq 5\text{, }&c=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable a cannot be equal to 5 since division by zero is not defined. Multiply both sides of the equation by a-5.

$$cx-5c=c\left(a-5\right)$$

Use the distributive property to multiply c by a-5.

$$cx-5c=ca-5c$$

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

$$ca-5c=cx-5c$$

Add 5c to both sides.

$$ca=cx-5c+5c$$

Combine -5c and 5c to get 0.

$$ca=cx$$

Divide both sides by c.

$$\frac{ca}{c}=\frac{cx}{c}$$

Dividing by c undoes the multiplication by c.

$$a=\frac{cx}{c}$$

Divide cx by c.

$$a=x$$

Variable a cannot be equal to 5.

$$a=x\text{, }a\neq 5$$

Solve for c

$$\left\{\begin{matrix}c=0\text{, }&a\neq 5\\c\in \mathrm{R}\text{, }&a=x\text{ and }x\neq 5\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a-5.

$$cx-5c=c\left(a-5\right)$$

Use the distributive property to multiply c by a-5.

$$cx-5c=ca-5c$$

Subtract ca from both sides.

$$cx-5c-ca=-5c$$

Add 5c to both sides.

$$cx-5c-ca+5c=0$$

Combine -5c and 5c to get 0.

$$cx-ca=0$$

Combine all terms containing c.

$$\left(x-a\right)c=0$$

Divide 0 by x-a.

$$c=0$$