Compute the following: $\displaystyle \sum_{j = 1}^6 \left[ -3 + 5(j - 1) \right]$.

$\begin{align}
\displaystyle \sum_{j = 1}^6 \left[ -3 + 5(j - 1) \right] & = \left[ -3 + 5(0) \right] + \left[ -3 + 5(1) \right] + \left[ -3 + 5(2) \right] + \left[ -3 + 5(3) \right] + \left[ -3 + 5(4) \right] + \left[ -3 + 5(5) \right] \\
& = -3 + 2 + 7 + 12 + 17 + 22 \\
\\
& = 57
\end{align}$