3x(x-8)=0

In order for two numbers to be multiplied together to equal zero,
one of them must be zero.

3x represents one number and (x-8) represents another number.

3x(x-8) says that the number 3x is multiplied by the number
represented by (x-8).

The =0 says that when those two numbers are multiplied you get 0.

Therefore one of them has to equal zero.  

But which one is 0?  Is it the 3x that equals 0 or the (x-8)?

We don't know.   So there are two possibilities.

First possibility:

The 3x is the one that equals 0:

3x = 0

Divide both sides by 3

 = 

x = 0

That's one solution.

Second possibility:

The (x-8) is the one that equals 0:

(x-8) = 0

x - 8 = 0
    x = 8

That's another solution.

So there are two solutions, 0 and 8

Edwin