#### Answer

$2x(x+6)(x-9)$

#### Work Step by Step

Since $2x$ is common to every term of the expression, we first factor out $2x$:
=$2x^{3}-6x^{2}-108x$
=$2x(x^{2}-3x-54)$
Now, we find out that the equation in the parenthesis represents a trinomial which can be factorized by using the rules of factoring trinomials:
=$2x(x^{2}-3x-54)$
=$2x(x^{2}+6x-9x-54)$
=$2x[x(x+6)-9(x+6)]$
=$2x[(x+6)(x-9)]$
=$2x(x+6)(x-9)$