Question 624896
<pre>
It's called the "zero-factor property", and it is common sense:

The principle is this:

If two quantities are multiplied and their product is 0, then one of 
them must be zero:

You have this:

                     (a+1)(a+2) = 0

This has two quantities (a+1) and (a+2) multiplied together and that
product equals 0.  Therefore there are two possibilities:

1.  (a+1) is 0 
2.  (a+2) is 0

Realize that unless one of those equals zero the product would not equal 0.



So to get both possible answers we set each one = 0

      Setting a+1 = 0, subtracting 1 from both sides gives a = -1 

      Setting a+2 = 0, subtracting 2 from both sides gives a = -2

Therefore there are two possible solutions a = -1 and a = -2.

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                          nē+3n-12 = 6

Get 0 on the right by adding -6 to both sides:

                          nē+3n-18 = 0

Factor the left side

                        (n+6)(n-3) = 0

As above to get both possible answers we set each one = 0

      Setting n+6 = 0, subtracting 6 from both sides gives n = -6 

      Setting n-3 = 0, adding 3 to both sides gives n = 3

Therefore there are two possible solutions n = -6 and n = 3.

Edwin</pre>