Question

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

Answer 1

`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 `(x-7)` = `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 `(x-7)`. 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(x-7)=0`:

For `x=0`
`0(-7)=0`
`0=0`
so it works.

For `x=7`
`7(7-7)=7(0)=0`
`0=0`
which also works.