Answer
$-16-\sqrt[]{35}$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL method, then,
\begin{array}{l}
\left( 2\sqrt[]{7}+3\sqrt[]{5} \right)\left( \sqrt[]{7}-2\sqrt[]{5} \right)
\\=
(2\sqrt[]{7})(\sqrt[]{7})+(2\sqrt[]{7})(-2\sqrt[]{5})+(3\sqrt[]{5})(\sqrt[]{7})+(3\sqrt[]{5})(-2\sqrt[]{5})
\\=
2\sqrt[]{49}-4\sqrt[]{35}+3\sqrt[]{35}-6\sqrt[]{25}
\\=
2\cdot7-\sqrt[]{35}-6\cdot5
\\=
14-\sqrt[]{35}-30
\\=
-16-\sqrt[]{35}
.\end{array}