To solve the equation \((3 - 5x)(3 + 5x) + (5x + 1)^2 = 7\), let's simplify and expand the left side step by step.

### Step 1: Expand \((3 - 5x)(3 + 5x)\)
This is a difference of squares:
\[
(3 - 5x)(3 + 5x) = 3^2 - (5x)^2 = 9 - 25x^2
\]

### Step 2: Expand \((5x + 1)^2\)
Using the square of a binomial formula:
\[
(5x + 1)^2 = (5x)^2 + 2(5x)(1) + 1^2 = 25x^2 + 10x + 1
\]

### Step 3: Combine the expanded expressions
Now substitute back into the equation:
\[
9 - 25x^2 + 25x^2 + 10x + 1 = 7
\]

Notice that the \(-25x^2\) and \(+25x^2\) cancel out:
\[
9 + 10x + 1 = 7
\]

### Step 4: Simplify the equation
Combine the constants:
\[
10 + 10x = 7
\]

### Step 5: Solve for \(x\)
Subtract 10 from both sides:
\[
10x = 7 - 10
\]
\[
10x = -3
\]

Now, divide by 10:
\[
x = -\frac{3}{10}
\]

### Conclusion
The solution to the equation \((3 - 5x)(3 + 5x) + (5x + 1)^2 = 7\) is:
\[
\boxed{-\frac{3}{10}}
\]