Answer
The possible dimensions of the trunk are $2x,\ 3x-2$ and $x+7$.
Work Step by Step
$6x^{3}+38x^{2}-28x=$
...factor out the GCF.
$=2x(3x^{2}+19x-14)$
...find factors of $ac$ that have a sum of $b$.
($ac=-42,\ b=19$)
$\left[\begin{array}{lll}
\text{Factors of 60 } & \text{Sum of factors} & \\
1\text{ and }-19 & -18 & \\
-1\text{ and }19 & 18 & \\
2\text{ and }-21 & -19 & \\
-2\text{ and }21 & 19 & \text{ is what we need}
\end{array}\right]$
...use the factors you found to rewrite $bx$.
$=2x(3x^{2}+21x-2x-14)$
...factor by grouping.
$=2x[3x(x+7)-2(x+7)]$
...use the Distributive Property.
$=2x(3x-2)(x+7)$
The possible dimensions of the trunk are $2x,\ 3x-2$ and $x+7$.
