Solve m^2x-m=16x+4

$$m ^ { 2 } x - m = 16 x + 4$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{1}{m-4}\text{, }&m\neq 4\\x\in \mathrm{C}\text{, }&m=-4\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 16x from both sides.

$$m^{2}x-m-16x=4$$

Add m to both sides.

$$m^{2}x-16x=4+m$$

Combine all terms containing x.

$$\left(m^{2}-16\right)x=4+m$$

The equation is in standard form.

$$\left(m^{2}-16\right)x=m+4$$

Divide both sides by m^{2}-16.

$$\frac{\left(m^{2}-16\right)x}{m^{2}-16}=\frac{m+4}{m^{2}-16}$$

Dividing by m^{2}-16 undoes the multiplication by m^{2}-16.

$$x=\frac{m+4}{m^{2}-16}$$

Divide 4+m by m^{2}-16.

$$x=\frac{1}{m-4}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{1}{m-4}\text{, }&m\neq 4\\x\in \mathrm{R}\text{, }&m=-4\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 16x from both sides.

$$m^{2}x-m-16x=4$$

Add m to both sides.

$$m^{2}x-16x=4+m$$

Combine all terms containing x.

$$\left(m^{2}-16\right)x=4+m$$

The equation is in standard form.

$$\left(m^{2}-16\right)x=m+4$$

Divide both sides by m^{2}-16.

$$\frac{\left(m^{2}-16\right)x}{m^{2}-16}=\frac{m+4}{m^{2}-16}$$

Dividing by m^{2}-16 undoes the multiplication by m^{2}-16.

$$x=\frac{m+4}{m^{2}-16}$$

Divide 4+m by m^{2}-16.

$$x=\frac{1}{m-4}$$

Solve for m

$$\left\{\begin{matrix}\\m=-4\text{, }&\text{unconditionally}\\m=4+\frac{1}{x}\text{, }&x\neq 0\end{matrix}\right.$$