X2 - x - 6 =
simplified. i know the answer is (x+2)(x-3), but i don't understand how the answer was achieved. can i get an explanation of this?

I had a lot of trouble with this when my algebra class started doing it,
a long time ago.

The key is this:  Look at the -6 at the end.  You have to find two factors
of that number that add up to the -1 in the middle.

Here are the possible factors of -6 :

-1 ... 6
+1 ... -6
-2 ... 3
+2 ... -3

Can you find a pair on the list that adds up to -1 ? 
How about +2 and -3 ?
Their product is -6 and their sum is -1.  That's what you need.

Now set up a couple of binomial factors like this:  (x) (x)
and write in the pair of numbers you found:  (x + 2) (x - 3)
That's the factored form of the original expression.

first anwser choice.

step-by-step explanation:

the greater/less or equal to symbol (> or < with the line at the bottom) is a closed/filled in circle.

when multiplying or dividing by a negative on both sides you have to flip the inequality sign. this rule only applies to multiplying or dividing by a negative number in inequality equations. this rule is really important.

-5c + 2 _< _27

subtract from both sides by 2

-5c _< _ 27

divide both sides by -5

c _< _ 5.4

flip the inequality sign

c _> _5.4

the only possible answer that would match the simplified inequality is the first answer choice