Answer
$(x+3) \left( x-3 \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
(x+3)(4x-1)-(x+3)(3x+2)
,$ get the $GCF.$ Then, divide the given expression and the $GCF.$ Express the answer as the product of the $GCF$ and the resulting quotient.
$\bf{\text{Solution Details:}}$
Factoring the $GCF=
x+3
,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(x+3) \left( \dfrac{(x+3)(4x-1)}{x+3}-\dfrac{(x+3)(3x+2)}{x+3}
\right)
\\\\=
(x+3) \left( (4x-1)-(3x+2)
\right)
\\\\=
(x+3) \left( 4x-1-3x-2
\right)
\\\\=
(x+3) \left( x-3 \right)
.\end{array}
