Two charges q and -3q are placed fixed on x-axis separated by distance d. Where should a third charge 2q be placed such that it will not experience any force?

Hint: Use Coulomb's law.
Step 1: Find the location of the third charge.
Here, let us keep the charge 2q at a distance r from A.
Thus, the charge 2q will not experience any force when the force of repulsion on it due to q is balanced by the force of attraction on it due to -3q, at B, where AB = d.
Step 2: Find the net force on the charge and put it equal to zero.
Thus, force of attraction by -3q = Force of repulsion by q
  2q×q4πε0x2=2q×3q4πε0(x+d)2
  x+d2=3x2
  x2+d2+2xd=3x2
   2xd=2x2-d2
2x2-2dx-d2=0
x=d2±3d2
Step 3: Choose the value with a positive sign.
(For negative sign, the position of the charge will be between q and -3q and hence is unadaptable.)
x=d2+3d2=d2(1+3) to the left of q.