Calculate X in Rectangle Area: Simplifying (3x+4)(3x-4)

To solve this problem, we start by recognizing that the expression for the area of the rectangle is given by the formula $(3x+4)(3x-4)$. This can be simplified using the difference of squares:

$(3x+4)(3x-4) = (3x)^2 - (4)^2 = 9x^2 - 16$.

The problem also provides the dimensions of the rectangle as 5 and 13. The area of the rectangle can therefore also be calculated as $5 \times 13 = 65$.

We set the two expressions for the area equal to each other to find $x$:

$9x^2 - 16 = 65$.

Next, we solve for $x$:

$9x^2 - 16 = 65$
$9x^2 = 65 + 16$
$9x^2 = 81$
$x^2 = \frac{81}{9}$
$x^2 = 9$
$x = \pm 3$.

Therefore, the value of $x$ is $\operatorname{\pm}3$.