If $-\dfrac{1}{2}$ is the solution of the equation 3x² + 2kx - 3 = 0, find the value of k.

Since, $-\dfrac{1}{2}$ is a solution of the equation 3x² + 2kx - 3 = 0, x = $-\dfrac{1}{2}$ satisfies the given equation.

Substituting x = $-\dfrac{1}{2}$ and solving for k we get:

$3\Big(-\dfrac{1}{2}\Big)^2 + 2k \Big(-\dfrac{1}{2}\Big) -3 = 0 \\[1em] \Rightarrow 3 \times \dfrac{1}{4} - k - 3 = 0 \\[1em] \Rightarrow -k = 3 - \dfrac{3}{4} \\[1em] \Rightarrow k = \dfrac{3}{4} - 3 \\[1em] \Rightarrow k = \dfrac{3 - 12}{4} \\[1em] \Rightarrow k = -\dfrac{9}{4}$

Hence, the value of k is $-\dfrac{9}{4}$