How to factor these numbers, it would be with a step by step

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!

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