# How do you solve x(x-7)=0?

Nov 1, 2015

$x = 0$
or
$x = 7$

#### Explanation:

The format of this queston is already in factored form. This makes it quite easy to solve for $x$. They key to this is to know that anything multiplied by $0$ is $0$. We have two things multiplied by each other:

$x$ multiplied by $\left(x - 7\right)$ = $0$

So, this means, that if either term is equal to zero, the whole equation will equal to zero.

The first term is just $x$, so $x = 0$ is the first solution.

The second term is $\left(x - 7\right)$. We need to set that equal to zero and solve for $x$.
$x - 7 = 0$
$x = 7$ which is our second solution.

To check, plugging back into $x \left(x - 7\right) = 0$:

For $x = 0$
$0 \left(- 7\right) = 0$
$0 = 0$
so it works.

For $x = 7$
$7 \left(7 - 7\right) = 7 \left(0\right) = 0$
$0 = 0$
which also works.