Solve mx=2(m+c)

$$m x = 2 ( m + c )$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{2c}{x-2}\text{, }&x\neq 2\\m\in \mathrm{C}\text{, }&c=0\text{ and }x=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by m+c.

$$mx=2m+2c$$

Subtract 2m from both sides.

$$mx-2m=2c$$

Combine all terms containing m.

$$\left(x-2\right)m=2c$$

Divide both sides by x-2.

$$\frac{\left(x-2\right)m}{x-2}=\frac{2c}{x-2}$$

Dividing by x-2 undoes the multiplication by x-2.

$$m=\frac{2c}{x-2}$$

Solve for c

$$c=\frac{m\left(x-2\right)}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by m+c.

$$mx=2m+2c$$

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

$$2m+2c=mx$$

Subtract 2m from both sides.

$$2c=mx-2m$$

Divide both sides by 2.

$$\frac{2c}{2}=\frac{m\left(x-2\right)}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$c=\frac{m\left(x-2\right)}{2}$$

Solve for m

$$\left\{\begin{matrix}m=\frac{2c}{x-2}\text{, }&x\neq 2\\m\in \mathrm{R}\text{, }&c=0\text{ and }x=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by m+c.

$$mx=2m+2c$$

Subtract 2m from both sides.

$$mx-2m=2c$$

Combine all terms containing m.

$$\left(x-2\right)m=2c$$

Divide both sides by x-2.

$$\frac{\left(x-2\right)m}{x-2}=\frac{2c}{x-2}$$

Dividing by x-2 undoes the multiplication by x-2.

$$m=\frac{2c}{x-2}$$