Resolve the Quadratic Equation: x² + 2x - 24 = -13 + (x-6)(x+6) + 7x

To solve the problem, we'll start by simplifying the right side of the equation.

1. Begin by expanding the difference of squares on the right side:
$(x-6)(x+6) = x^2 - 6^2 = x^2 - 36$.

2. Substitute back into the equation:
$x^2 + 2x - 24 = -13 + (x^2 - 36) + 7x$.

3. Simplify the right side:
Combine like terms:
$-13 + x^2 - 36 + 7x = x^2 + 7x - 49$.

4. Now the equation is:
$x^2 + 2x - 24 = x^2 + 7x - 49$.

5. Subtract $x^2$ from both sides to eliminate $x^2$:
$2x - 24 = 7x - 49$.

6. Move all terms involving $x$ to one side and constants to the other side:
Subtract $7x$ from both sides:
$2x - 7x = -49 + 24$.
Simplify to:
$-5x = -25$.

7. Solve for $x$ by dividing both sides by $-5$:
$x = \frac{-25}{-5} = 5$.

Therefore, the solution to the problem is $x = 5$.