Solve 2ax-(4a+2)+4/x=0

$$2 a x - ( 4 a + 2 ) + \frac { 4 } { x } = 0$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{1}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&x=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$2axx-\left(4a+2\right)x+4=0$$

Multiply x and x to get x^{2}.

$$2ax^{2}-\left(4a+2\right)x+4=0$$

Use the distributive property to multiply -1 by 4a+2.

$$2ax^{2}+\left(-4a-2\right)x+4=0$$

Use the distributive property to multiply -4a-2 by x.

$$2ax^{2}-4ax-2x+4=0$$

Add 2x to both sides. Anything plus zero gives itself.

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

Subtract 4 from both sides.

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

Combine all terms containing a.

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

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

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

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

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

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

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

Solve for a

$$\left\{\begin{matrix}a=\frac{1}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$2axx-\left(4a+2\right)x+4=0$$

Multiply x and x to get x^{2}.

$$2ax^{2}-\left(4a+2\right)x+4=0$$

Use the distributive property to multiply -1 by 4a+2.

$$2ax^{2}+\left(-4a-2\right)x+4=0$$

Use the distributive property to multiply -4a-2 by x.

$$2ax^{2}-4ax-2x+4=0$$

Add 2x to both sides. Anything plus zero gives itself.

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

Subtract 4 from both sides.

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

Combine all terms containing a.

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

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

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

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

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

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

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

Solve for x

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