Expanding the left side of the equation:

(x+5)^2 + (x-7)(x+7)
= (x+5)(x+5) + (x^2 + 7x - 7x - 49)
= x^2 + 5x + 5x + 25 + x^2 - 49
= 2x^2 + 10x - 24

Now the equation becomes:

2x^2 + 10x - 24 = 6x - 19

Subtracting 6x and adding 19 to both sides:

2x^2 + 4x - 5 = 0

This is a quadratic equation that can be factored as:

(2x - 5)(x + 1) = 0

Setting each factor to zero:

2x - 5 = 0
2x = 5
x = 5/2

x + 1 = 0
x = -1

Therefore, the solutions are x = 5/2 and x = -1.