Step-by-step explanation:

16x2 + 4x - 2 =0.

  2 • (8x2 + 2x - 1) =0.

8x^2 + 2x - 1= 0/2.

8x^2 + 2x - 1 = 0.

Factoring  8x2 + 2x - 1 

The first term is,  8x2  its coefficient is  8 .

The middle term is,  +2x  its coefficient is  2 .

The last term, "the constant", is  -1 

Step-1 : MULTIPLY the coefficient of the first term by the constant   8 • -1 = -8 

Step-2 : FIND two FACTORS of  -8  whose sum equals the coefficient of the middle term, which is   2 .

-2   +   4   =   2   That's it

Step-3 : Rewrite the polynomial SPLITTING the middle term using the two factors found in step 2 above,  -2  and  4 

                     8x2 - 2x + 4x - 1

Step-4 : Add up the first 2 terms, pulling out like factors :

                    2x • (4x-1)

              Add up the last 2 terms, pulling out common factors :

                     1 • (4x-1)

Step-5 : Add up the four terms of step 4 :

                    (2x+1)  •  (4x-1)

             Which is the desired factorization

2x+1 =0 (or) 4x-1 =0.

2x=-1 (or) 4x = 1

x= -1/2 (or) x= 1/4.