​ What is the missing term in the factorization?

Let  m   be the missing term  and we have that

100x^2  - 36 =  4(5x + m) (5x - 3)       divide both sides by 4

25x^2  -  9   =   (5x + m ) (5x - 3)        expand the right side

25x^2  -  9  =   25x^2  + 5mx - 15x  -  3m   subtract  25x^2  from both sides

-9  =  5mx   - 15x   -  3m

-9  =  (5m - 15)x   -  3m

Since there is no x term  on the left side, we can equate this

0x  =  (5m - 15)x

So

5m - 15  = 0       add 15 to both sides

5m  = 15    divide both sides by  5

m  = 3