Gravitational Force [I'm not asking you to work a problem for me]?

Question

The problem I'm working on states:
Objects with masses of 120 kg (m1) and a 420 kg (m2) are separated by 0.310 m (m3).
(a) Find the net gravitational force exerted by these objects on a 50.0 kg object placed midway between them.
[The answer I found is 4.1642E-5]
(b) At what position (other than infinitely remote ones) can the 50.0 kg object be placed so as to experience a net force of zero?
___ m from the 420 kg mass

To solve B, would I set the net gravitational force equal to zero? ((Gm1m3)/r^2) + ((Gm2m3)/r^2) = 0, and solve for r?

Answer 1

If the distance to m2 is r, than the distance to m1 is (0.31-r). But it's easier to solve if you use r1 and r2 for the distances and solve for the ratio between them, then solve them individually using r1 + r2 = 0.31.

Answer 2

B)

Place the m2 at origin and m3 at a distance r1 from m2 and m1 at distance r2 from m3 and away from m2. i.e. m3 is in between m2 and m1.

Force acting on m3 by m2 and m1 must be equal and opposite.

G m2 m3 / r1^2 = G m1m3 /r2^2

m2 / r1^2 = m1 /r2^2

[r1/r2]^2 = m2 /m1 = 420 / 120

[r1/r2 =1.87
r1 = 1.87 r2 m