If 4x^2-100=0, the roots are

This is a difference of 2 perfect squares where you can factor x^2-y^2 = (x-y) (x+y) so

also if it is equal to zero and you factor, then each factor is assumed set to zero exg

xy=0 then assume x and/or y=0 so

4x^2-100

(2x) ^2 - (10) ^2 = (2x-10) (2x+10) = 0

so the roots are (2x-10) and (2x+10)

(solution is 5 and - 5)