really need help

[F.B]

I have a question on universal gravitation, it's sort of really hard, especially since i forgot some math rules.

At a certain point between the Earth and the Moon, the net gravitational force exerted on an object by Earth and the Moon is zero. The Earth-moon centre to centre separation is 3.84 x 10^8m. The mass of the moon is 1.2% the mass of the earth.
a) Where is this point located? Are there any such points?

I know there are points because theres an answer. Anyways heres what i did.

FG=0

GMem/(Re-m)^2=G x 0.012Me x m/(Rm-m)^2

After cancelling everything out. I do this:

1/(Re-m)^2= 0.012Me/(Rm-m)^2
Now i still have two unknowns so i solve for Rm-m

(3.84 x 10^8 - Re-m)^2= 0.012Re-m^2

Heres my problem i dont know how what to do with the bracket. If i expand it and then do quadratic formula i dont get the right answer.

So can anyone please help me and tell me if i did anything wrong.

[Doc Al]

Your notation is a bit hard to follow. (What's "Re-m"?) But I suspect you have the right idea. To solve your equation, take the square root of both sides.

I'd write the equation this way. Calling D the distance between the centers and x the distance from the zero force point to the earth:
\frac{G M_E m}{x^2} = 0.012 \frac{G M_E m}{(D - x)^2}

Which becomes:
0.012 x^2 = (D - x)^2