Let's simplify and solve the given expression step by step:

### Given Expression:
\[
7 \tan^2(x) - 7 \sec^2(x) + 7
\]

### Step 1: Factor out the common term
The expression can be factored as:
\[
7(\tan^2(x) - \sec^2(x)) + 7
\]

### Step 2: Use the Pythagorean identity
We know from trigonometric identities that:
\[
\sec^2(x) = 1 + \tan^2(x)
\]
Thus, we can substitute \(\sec^2(x)\) into the expression:
\[
\tan^2(x) - \sec^2(x) = \tan^2(x) - (1 + \tan^2(x))
\]

Simplifying the expression:
\[
\tan^2(x) - 1 - \tan^2(x) = -1
\]

### Step 3: Substitute back and simplify
Now substitute \(-1\) back into the expression:
\[
7(-1) + 7 = -7 + 7 = 0
\]

### Final Answer:
The value of the expression is \(\boxed{0}\).

Would you like a more detailed explanation or have any other questions? Here are some related questions that might interest you:

1. How does the identity \(\sec^2(x) = 1 + \tan^2(x)\) derive from the Pythagorean theorem?
2. What are other important trigonometric identities used in simplifications?
3. How do you solve equations involving \(\tan(x)\) and \(\sec(x)\) for specific angles?
4. What are the key steps to factor and simplify trigonometric expressions?
5. How would the solution change if we used different trigonometric identities?

**Tip:** Always remember to check if there are any common trigonometric identities that can simplify your expression before diving into calculations.

Learn how to simplify and solve the expression 7 tan^2(x) - 7 sec^2(x) + 7 step-by-step with a detailed explanation. This problem involves trigonometric identities and their applications, suitable for high school students studying trigonometry.

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