The problem is to simplify the expression $9x^2(2x+7)-12x(2x+7)$.

1. Problem Description

The problem is to simplify the expression $9x^2(2x+7)-12x(2x+7)$.

2. Solution Steps

First, we can factor out the common term $(2x+7)$ from both terms in the expression:

$9x^2(2x+7) - 12x(2x+7) = (2x+7)(9x^2 - 12x)$

Next, we can factor out the common term $3x$ from the second factor $(9x^2 - 12x)$:

$9x^2 - 12x = 3x(3x - 4)$

Therefore,

$(2x+7)(9x^2 - 12x) = (2x+7)(3x(3x-4))$

Rearrange the terms to get:

$3x(2x+7)(3x-4)$

Now, we can expand the expression:

$3x(2x+7)(3x-4) = 3x(6x^2 - 8x + 21x - 28) = 3x(6x^2 + 13x - 28)$

Finally, we distribute the $3x$ term:

$3x(6x^2 + 13x - 28) = 18x^3 + 39x^2 - 84x$

3. Final Answer

$18x^3 + 39x^2 - 84x$