The given equation is:

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

However, it seems that there might be a typo or some confusion in the equation because it doesn't look like a typical form of an equation. It could be broken down into two parts or might need clarification. I'll assume three possibilities based on different interpretations for clarification:
1. Splitting the equation into two separate equations.
2. Setting the expressions equal to each other.
3. Derive one logical mathematical expression from the equation as it is.

### Option 1: Splitting It into Two Separate Equations

If you are considering the equation to be split into two separate parts:

1. \[ -2(2x+7)^2 = 2 \]
2. \[ 2 - 2(2x+7)^2 = 2 \]

**Solving the first equation:**
\[ -2(2x+7)^2 = 2 \]

Divide both sides by -2:
\[ (2x+7)^2 = -1 \]

Since the square of a real number can't be negative, there is no real solution for \( x \) in this equation.

**Solving the second equation:**
\[ 2 - 2(2x+7)^2 = 2 \]

Subtract 2 from both sides:
\[ -2(2x+7)^2 = 0 \]

Divide both sides by -2:
\[ (2x+7)^2 = 0 \]

Taking the square root of both sides:
\[ 2x+7 = 0 \]

Solving for \( x \):
\[ 2x = -7 \]

\[ x = -\frac{7}{2} \]

So, for these possible separate equations, \( x = -\frac{7}{2} \) is the solution for the second equation, and there is no real solution for the first one.

### Option 2: Setting the Expressions Equal to Each Other

If you intend to set the left side of the first part equal to the right side of the second part:
\[ -2(2x+7)^2 = 2 - 2(2x+7)^2 \]

Adding \( 2(2x+7)^2 \) to both sides:
\[ 0 = 2 \]

This results in a contradiction, implying there is no value of \( x \) satisfying the equation.

### Option 3: Combining

If there's some combined logical way to interpret the given equation:

Let's consider simplifying:

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

Combining like terms:
\[ -4(2x+7)^2 + 2 = 2 \]

Subtract 2 from both sides:
\[ -4(2x+7)^2 = 0 \]

Divide by -4:
\[ (2x+7)^2 = 0 \]

Taking the square root of both sides:
\[ 2x + 7 = 0 \]

Solving for \( x \):
\[ 2x = -7 \]

\[ x = -\frac{7}{2} \]

Therefore, the value of \( x \) is \( x = -\frac{7}{2} \).