## Solving the Quadratic Equation: (x^2-7)^2 - 5(x^2-7) + 6 = 0

This equation may seem complicated at first glance, but it can be solved using a simple substitution technique. Here's how:

### 1. Substitution:

Let's simplify the equation by substituting a new variable. Let **y = x^2 - 7**. Now the equation becomes:

**y^2 - 5y + 6 = 0**

### 2. Factoring:

This is a standard quadratic equation. We can factor it easily:

**(y - 2)(y - 3) = 0**

This gives us two possible solutions for 'y':

**y = 2****y = 3**

### 3. Back Substitution:

Now, we need to substitute back the original expression for 'y':

**x^2 - 7 = 2****x^2 - 7 = 3**

Solving these equations:

**x^2 = 9****x^2 = 10**

### 4. Finding the Solutions:

Taking the square root of both sides for each equation:

**x = ± 3****x = ± √10**

### Conclusion:

Therefore, the solutions to the equation (x^2-7)^2 - 5(x^2-7) + 6 = 0 are:

**x = 3****x = -3****x = √10****x = -√10**