Three charges are placed on the x-axis: q1=q at x=0, q2=-3q at x=d, and q3=2q at x. Find the position x for q3 such that the net force on it is zero.

Let the charge $q_1 = q$ be placed at the origin, $x_1 = 0$.
Let the charge $q_2 = -3q$ be placed at $x_2 = d$.
Let the third charge $q_3 = 2q$ be placed at an unknown position $x$.

For the net force on $q_3$ to be zero, the forces due to $q_1$ and $q_2$ must be equal in magnitude and opposite in direction.
Since $q_1$ and $q_2$ have opposite signs ($q$ is positive, $-3q$ is negative), the equilibrium point cannot be between them. If $q_3$ (positive) is between $q_1$ and $q_2$, $q_1$ would repel it to the right, and $q_2$ would attract it to the right. Both forces would be in the same direction, so they cannot cancel.
Therefore, the equilibrium point must be outside the region $0 < x < d$.

Also, for the forces to cancel, the third charge must be closer to the charge with the smaller magnitude. Here, $|q_1| = |q|$ and $|q_2| = |-3q| = 3|q|$. Since $|