Answer
$(x+1)(25x+64)$
Work Step by Step
Rearranging the terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
89x+64+25x^2
\\\\=
25x^2+89x+64
.\end{array}
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
25x^2+89x+64
\end{array} has $ac=
25(64)=1600
$ and $b=
89
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
25,64
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
25x^2+25x+64x+64
.\end{array}
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(25x^2+25x)+(64x+64)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
25x(x+1)+64(x+1)
.\end{array}
Factoring the $GCF=
(x+1)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(x+1)(25x+64)
.\end{array}