How do you factor the expression 7x(2x + 3) + (2x + 3)?

$\left(7 x + 1\right) \left(2 x + 3\right)$
since we have $2 x + 3$ in both sets of brackets, we have a common theme. to expand the brackets, a "1" is implied at the beginning of the second set of brackets.
$7 x \left(2 x + 3\right) + 1 \left(2 x + 3\right)$
you can now make $\left(7 x + 1\right) \left(2 x + 3\right)$ from that.