6x^2 + 5x - 6 is not a number; it's a polynomial expression. You are asked to factor it.
Look at the last coefficient (-6) and then at the first (6). You can form a variety of possible "rational roots" from variations of -6 over 6:
Examples: plus or minus 1/6, plus or minus 2/3, plus or minus 1, and so on. Note that 6 has the following prime factors: {1, 2, 3, 6}.
I like to use synthetic division on problems such as this one. Are you familiar with s. d.?
Suppose we check whether -2/3 is a root (I just picked that out of a blue sky).
Set up synth. div.:
__________________
-2/3 / 6 5 -6
-4 -2/3
--------------------
6 1 20/3
Since the remainder is not zero, -2/3 is not a root of the given polynomial.
You could find the factors by continuing to use synth. div.
Note that if x= a is a root, then x-a is a factor.
You could find the roots using the quadratic formula:
-b plus or minus sqrt( b^2 - 4(a)(c) )
x = ----------------------------------------------------
2a
Here a=6, b=5 and c= -6
Then
-b plus or minus sqrt( b^2 - 4(a)(c) )
x = ---------------------------------------------------- becomes
2a
-5 plus or minus sqrt( 5^2 - 4(6)(-6) )
x = ----------------------------------------------------
2(6)
-5 plus or minus sqrt( 25 + 144)
= -------------------------------------------------------
12
-5 plus or minus 13
= ------------------------------------- = 8/12, or 2/3
12
or x = -18/12 = -3/2
The factors are then 3x - 2 and 2x + 3. Try them!
