Multiply: (5x + 3) by (7x + 2)

To multiply, we will use distributive law as follows:

$(5 x+3)(7 x+2)$

$=5 x(7 x+2)+3(7 x+2)$

$=(5 x \times 7 x+5 x \times 2)+(3 \times 7 x+3 \times 2)$

$=\left(35 x^{2}+10 x\right)+(21 x+6)$

$=35 x^{2}+10 x+21 x+6$

$=35 x^{2}+31 x+6$

Thus, the answer is $35 x^{2}+31 x+6$.