The problem requires us to multiply and simplify the expression $(5x\sqrt{3x})(-6\sqrt{21xy})$. We assume that all variables represent non-negative numbers.

1. Problem Description

The problem requires us to multiply and simplify the expression $(5x\sqrt{3x})(-6\sqrt{21xy})$. We assume that all variables represent non-negative numbers.

2. Solution Steps

First, we multiply the coefficients and the radicals:

$(5x\sqrt{3x})(-6\sqrt{21xy}) = (5x)(-6)(\sqrt{3x})(\sqrt{21xy})$

$= -30x\sqrt{(3x)(21xy)}$

$= -30x\sqrt{63x^2y}$

Next, we simplify the radical by factoring out perfect squares:

$\sqrt{63x^2y} = \sqrt{9 \cdot 7 \cdot x^2 \cdot y} = \sqrt{9x^2 \cdot 7y} = \sqrt{9}\sqrt{x^2}\sqrt{7y} = 3x\sqrt{7y}$.

Now we substitute this back into the expression:

$-30x\sqrt{63x^2y} = -30x(3x\sqrt{7y}) = -90x^2\sqrt{7y}$.

3. Final Answer

$-90x^2\sqrt{7y}$