To solve for x in the equation 300/x(x+10) = 3/20, we can first simplify the equation by multiplying both sides by 20 to get rid of the fraction:

20 300/x(x+10) = 20 3/20
6000/x(x+10) = 3
6000 = 3x(x+10)

Next, we can expand the equation and set it equal to zero to solve for x:

6000 = 3x^2 + 30x
3x^2 + 30x - 6000 = 0

Now, we can factor out a 3 from the equation:

3(x^2 + 10x - 2000) = 0

Then, we can factor the quadratic equation x^2 + 10x - 2000 to find the solution for x:

3(x + 50)(x - 40) = 0

Setting each factor equal to zero gives us:

x + 50 = 0 OR x - 40 = 0

x = -50 OR x = 40

Therefore, the solutions for x are x = -50 or x = 40.