Answer
$=(x-4)(3x-5)$.
Work Step by Step
The given expression is
$=3(x-2)^{2}-5(x-2)-2$
Substitute $x-2=u$.
$=3(u)^2-5u-2$
Simplify.
$=3u^2-5u-2$
Rewrite $-5u$ as $-6u+1u$.
$=3u^2-6u+1u-2$
Factor.
$=3u(u-2)+1(u-2)$
$=(u-2)(3u+1)$.
Substitute back $u=x-2$.
$=((x-2)-2)(3(x-2)+1)$.
Simplify.
$=(x-2-2)(3x-6+1)$.
$=(x-4)(3x-5)$.
