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