EDWIN'S EXPLANATION:
How do I solve this (below) using factoring?
I appreciate your help so much. Thank you.
Rule for factoring a trinomial whose coefficient
of the squared letter is understood as +1.
From right to left look at these:
P. The last number in absolute value.
Q. The sign before the last number.
R. The middle coefficient in absolute value.
S. The sign before the middle coefficient.
1. Think of a pair of factors of P, such that when you
do the operation determined by Q to them, you get R.
Then write
(x )(x )
2. Place the two factors where the #'s are below:
(x #)(x #)
3. Place the sign from S before the larger of the #'s
4. If Q is +, place the same sign as S on the smaller of the #'s.
5. If Q is -, place the opposite sign from S in the smaller of the #'s.
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Let's go through your problem with these to factor
the left side:
From right to left look at these:
P. The last number in absolute value. THIS IS 27
Q. The sign before the last number. THIS IS -
R. The middle coefficient in absolute value. THIS IS 6
S. The sign before the middle coefficient. THIS IS +
1. Think of a pair of factors of P, such that when you
do the operation determined by Q to them, you get R.
THESE ARE 9 AND 3, because 9x3=27 and 9-3=6
Then write
(x )(x )
2. Place the two factors where the #'s are below:
(x #)(x #)
SO WE WRITE (x 9)(x 3)
3. Place the sign from S before the larger of the #'s
THE LARGER IS 9, AND THE SIGN FROM S is +,
SO WE WRITE: (x + 9)(x 3)
4. If Q is +, place the same sign on the smaller of the #'s.
IT'S NOT.
5. If Q is -, place the opposite sign in the smaller of the #'s.
SO WE WRITE (x + 9)(x - 3)
Now we have gone from this:
to this
Now to use the zero-factor principle:
Each of the parentheses on the left
represents a number. They are multipled
to get 0 on the right. In order to get a
0 on the right one of those two parentheses
must equal 0. It could be either one, so
we get two solutions, by setting each
factor on the left = 0 and solving for x
gives the solution 
gives the solution 
Edwin
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