Answer
Particle C should be placed at the position $x = -5.0~d$
Work Step by Step
The gravitational force on A due to B is directed in the positive x direction.
For the net gravitational force on A to be zero, the gravitational force on A due to C must be directed in the negative x direction. Particle C must be placed to the left of particle A.
For the net gravitational force on A to be zero, the gravitational force on A due to C must be equal in magnitude to the gravitational force on A due to B.
Let $r$ be the distance of C to the left of A. We can find $r$:
$\frac{G~m_B~m_A}{d^2} = \frac{G~m_C~m_A}{r^2}$
$r^2 = \frac{m_C~d^2}{m_B}$
$r^2 = \frac{75.0~m_A~d^2}{3.00~m_A}$
$r^2 = 25.0~d^2$
$r = 5.0~d$
Since particle A is located at the origin, particle C should be placed at the position $x = -5.0~d$
