Let's simplify the left side of the equation step by step:

(4x + 3)(5 - x) - x^2
= 20x - 4x^2 + 15 - 3x - x^2
= 20x - 4x^2 + 15 - 3x - x^2
= 20x - 4x^2 - x^2 - 3x + 15
= 20x - 5x^2 - 3x + 15

Now we have:
20x - 5x^2 - 3x + 15 = 8x + 19

Combine like terms:
17x - 5x^2 = 8x + 19
-5x^2 + 17x - 8x - 19 = 0
-5x^2 + 9x - 19 = 0

Therefore, the simplified form of the equation is -5x^2 + 9x - 19 = 0.