# How do you solve 12x^2 - 6x = 0?

Mar 13, 2018

See a solution process below:

#### Explanation:

First, factor an $6 x$ from each term on the left side of the equation:

$\left(6 x \cdot 2 x\right) - \left(6 x \cdot 1\right) = 0$

$6 x \left(2 x - 1\right) = 0$

Now, solve each term on the left for $0$:

Solution 1:

$6 x = 0$

$\frac{6 x}{\textcolor{red}{6}} = \frac{0}{\textcolor{red}{6}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}} x}{\cancel{\textcolor{red}{6}}} = 0$

$x = 0$

Solution 2:

$2 x - 1 = 0$

$2 x - 1 + \textcolor{red}{1} = 0 + \textcolor{red}{1}$

$2 x - 0 = 1$

$2 x = 1$

$\frac{2 x}{\textcolor{red}{2}} = \frac{1}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}} = \frac{1}{2}$

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

The Solution Set Is: $x = \left\{0 , \frac{1}{2}\right\}$