To simplify the given expression \((2x + 7)^2 + (-2x - 3)^2\), we need to expand each squared term and then combine like terms. Let's do this step-by-step.

First, expand \((2x + 7)^2\):

\[
(2x + 7)^2 = (2x + 7)(2x + 7)
\]

Using the distributive property (FOIL method):

\[
(2x + 7)(2x + 7) = 2x \cdot 2x + 2x \cdot 7 + 7 \cdot 2x + 7 \cdot 7
\]

\[
= 4x^2 + 14x + 14x + 49
\]

\[
= 4x^2 + 28x + 49
\]

Next, expand \((-2x - 3)^2\):

\[
(-2x - 3)^2 = (-2x - 3)(-2x - 3)
\]

Using the distributive property (FOIL method):

\[
(-2x - 3)(-2x - 3) = (-2x) \cdot (-2x) + (-2x) \cdot (-3) + (-3) \cdot (-2x) + (-3) \cdot (-3)
\]

\[
= 4x^2 + 6x + 6x + 9
\]

\[
= 4x^2 + 12x + 9
\]

Now, add the two expanded expressions together:

\[
(2x + 7)^2 + (-2x - 3)^2 = (4x^2 + 28x + 49) + (4x^2 + 12x + 9)
\]

Combine like terms:

\[
= 4x^2 + 4x^2 + 28x + 12x + 49 + 9
\]

\[
= 8x^2 + 40x + 58
\]

So, the simplified form of the given expression is:

\[
8x^2 + 40x + 58
\]