Answer
$(z+1) \left( 3z-1 \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
(z+1)(z-4)+(z+1)(2z+3)
,$ 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 $GCF=
z+1
,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(z+1) \left( \dfrac{(z+1)(z-4)}{z+1}+\dfrac{(z+1)(2z+3)}{z+1} \right)
\\\\=
(z+1) \left( (z-4)+(2z+3) \right)
\\\\=
(z+1) \left( z-4+2z+3 \right)
\\\\=
(z+1) \left( 3z-1 \right)
.\end{array}
