Simplify and Solve: Find x in (x-4)(x+4) - 5x = -8 - x² - 25x + 4x - 38

To solve the given equation $(x-4)(x+4) - 5x = -8 - x^2 - 25x - 38 + 4x$, we'll follow these steps:

Step 1: Expand the expression on the left side using the difference of squares formula:
$(x-4)(x+4) = x^2 - 16$.
Substituting, we get:
$x^2 - 16 - 5x$.

Step 2: Simplify the right-hand side expression:
Combine like terms: $-x^2 - 25x + 4x - 8 - 38$ becomes
$-x^2 - 21x - 46$.

We now have the equation:
$x^2 - 16 - 5x = -x^2 - 21x - 46$.

Step 3: Bring all terms to one side to equate to zero:
Add $x^2$ and add $21x$ to both sides:
$x^2 + x^2 - 5x + 21x - 16 + 46 = 0$.
This simplifies to:
$2x^2 + 16x + 30 = 0$.

Step 4: Simplify further by factoring or using the quadratic formula. Factor out the common term:
$x^2 + 8x + 15 = 0$.
This factors to:
$(x+5)(x+3) = 0$.

Setting each factor to zero gives:
$x+5 = 0$ or $x+3 = 0$.
Thus, $x = -5$ or $x = -3$.

Therefore, the solution to the equation is $x = -5, -3$.