Solve ax^2-2abx=0

$$a x ^ { 2 } - 2 a b x = 0$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=0\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=2b\text{ or }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine all terms containing a.

$$\left(x^{2}-2bx\right)a=0$$

Divide 0 by x^{2}-2bx.

$$a=0$$

Solve for b (complex solution)

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

Steps for Solving Linear Equation

Subtract ax^{2} from both sides. Anything subtracted from zero gives its negation.

$$-2abx=-ax^{2}$$

The equation is in standard form.

$$\left(-2ax\right)b=-ax^{2}$$

Divide both sides by -2ax.

$$\frac{\left(-2ax\right)b}{-2ax}=-\frac{ax^{2}}{-2ax}$$

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

$$b=-\frac{ax^{2}}{-2ax}$$

Divide -ax^{2} by -2ax.

$$b=\frac{x}{2}$$

Solve for a

$$\left\{\begin{matrix}\\a=0\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&x=2b\text{ or }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine all terms containing a.

$$\left(x^{2}-2bx\right)a=0$$

Divide 0 by x^{2}-2bx.

$$a=0$$

Solve for b

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

Steps for Solving Linear Equation

Subtract ax^{2} from both sides. Anything subtracted from zero gives its negation.

$$-2abx=-ax^{2}$$

The equation is in standard form.

$$\left(-2ax\right)b=-ax^{2}$$

Divide both sides by -2ax.

$$\frac{\left(-2ax\right)b}{-2ax}=-\frac{ax^{2}}{-2ax}$$

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

$$b=-\frac{ax^{2}}{-2ax}$$

Divide -ax^{2} by -2ax.

$$b=\frac{x}{2}$$