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

##x=0## or ##x=7##

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.