100 times my number is equal to the square of my number divided by 4. What are possible values of my number?

We have

100N =N^2 / 4   multiply both sides by 4

400N = N^2       rearrange

N^2 - 400N = 0   factor

N(N - 400) = 0     and setting both factors to 0, we have that  N = 0 or N = 400