# How do you factor and solve x(2x-1)=0?

Aug 1, 2016

$x = 0 \mathmr{and} x = \frac{1}{2}$
Factor the equation and solve for each factor separately
$x = 0 \mathmr{and} 2 x - 1 = 0$

#### Explanation:

$x = 0 \text{ or } 2 x - 1 = 0$

Solve $2 x - 1 = 0$ by working backwards PE SADM
add the opposite of -1 to both sides

$2 x - 1 + 1 = 0 + 1$

$\left(- 1 + 1 = 0\right)$

Divide both sides by 2 the opposite of multiplying by 2

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

$\left(\frac{2}{2} = 1\right)$

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

As this equation has two factors with $x$, it has two possible solutions.

The first solution is $x = 0$
The second is $x = \frac{1}{2}$