Answer
$23x-5x\sqrt[]{15}$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL method, then,
\begin{array}{l}
\left( \sqrt[]{5x}-2\sqrt[]{3x} \right)\left( \sqrt[]{5x}-3\sqrt[]{3x} \right)
\\=
(\sqrt[]{5x})(\sqrt[]{5x})+(\sqrt[]{5x})(-3\sqrt[]{3x})+(-2\sqrt[]{3x})(\sqrt[]{5x})+(-2\sqrt[]{3x})(-3\sqrt[]{3x})
\\=
\sqrt[]{25x^2}-3\sqrt[]{15x^2}-2\sqrt[]{15x^2}+6\sqrt[]{9x^2}
\\=
5x-5\sqrt[]{15x^2}+6\cdot3x
\\=
5x-5x\sqrt[]{15}+18x
\\=
23x-5x\sqrt[]{15}
.\end{array}
