We are asked to multiply and simplify the expression $7\sqrt{x}(3\sqrt{5}-9\sqrt{x})$. We assume that all variables represent nonnegative numbers.

1. Problem Description

We are asked to multiply and simplify the expression $7\sqrt{x}(3\sqrt{5}-9\sqrt{x})$. We assume that all variables represent nonnegative numbers.

2. Solution Steps

First, distribute the $7\sqrt{x}$ to both terms inside the parenthesis:

$7\sqrt{x}(3\sqrt{5}-9\sqrt{x}) = 7\sqrt{x} \cdot 3\sqrt{5} - 7\sqrt{x} \cdot 9\sqrt{x}$

$= 21\sqrt{x}\sqrt{5} - 63\sqrt{x}\sqrt{x}$

$= 21\sqrt{5x} - 63\sqrt{x^2}$

Since $x$ is nonnegative, $\sqrt{x^2} = x$. Therefore,

$= 21\sqrt{5x} - 63x$

3. Final Answer

$21\sqrt{5x} - 63x$