Factoring question!!

 -3x^3+5x+2  =

-(x+1) (3 x^2 - 3x - 2)

Here's the explanation:

-3x^3+5x+2        write the middle term as 3x + 2x.......so we have

-3x^3 + 3x + 2x + 2       factor by grouping

3x(1 -x^2) + 2(x + 1)

3x (1 + x) (1 -x) + 2 (x + 1)

3x (x + 1) (1 - x) + 2 (x + 1)   factor out the (x + 1)

(x + 1) [ 3x (1 -x) +  2 )

(x + 1) (-3x^2 + 3x + 2)  factor out a " -1 " from the second term

(x + 1) (-1)(3x^2 - 3x - 2 )

-(x + 1)(3x^2 - 3x - 2)

why do you write the middle term as 3x+2x ??? This doesnt add up to -6. Where do you get those numbers from?

Huh???....I want to write 5x  in a different form  =   3x + 2x

Where did you get -6  from  ?????

The terms a and c should be multiplied together and those terms have to add up to 5. Thats what Ive read.