Solve a^2x-2=4x+a

$$a ^ { 2 } x - 2 = 4 x + a$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{1}{a-2}\text{, }&a\neq 2\\x\in \mathrm{C}\text{, }&a=-2\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 4x from both sides.

$$a^{2}x-2-4x=a$$

Add 2 to both sides.

$$a^{2}x-4x=a+2$$

Combine all terms containing x.

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

Divide both sides by a^{2}-4.

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

Dividing by a^{2}-4 undoes the multiplication by a^{2}-4.

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

Divide 2+a by a^{2}-4.

$$x=\frac{1}{a-2}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{1}{a-2}\text{, }&a\neq 2\\x\in \mathrm{R}\text{, }&a=-2\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 4x from both sides.

$$a^{2}x-2-4x=a$$

Add 2 to both sides.

$$a^{2}x-4x=a+2$$

Combine all terms containing x.

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

Divide both sides by a^{2}-4.

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

Dividing by a^{2}-4 undoes the multiplication by a^{2}-4.

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

Divide 2+a by a^{2}-4.

$$x=\frac{1}{a-2}$$

Solve for a

$$\left\{\begin{matrix}\\a=-2\text{, }&\text{unconditionally}\\a=2+\frac{1}{x}\text{, }&x\neq 0\end{matrix}\right.$$