(c+6)(3a-4) + (a-c)(1+c+a) - 3ac + 24 + 5c - 19a = ac^2 - c^2

Expanding the terms:
3ac + 18a - 4c - 24 + a - ac - c^2 - c^2 - ac + a^2 - ac + c^2 + a - c - 3ac + 24 + 5c - 19a = ac^2 - c^2

Simplifying the terms:
-ac + 18a - 4c + a - c^2 + a^2 + a - c - 3ac + 24 + 5c - 19a = ac^2 - c^2

Combining like terms:
18a + a + a + a - 19a - 3ac - ac - ac - 4c - c - c + 5c - c^2 + a^2 - c^2 = ac^2 - c^2

22a - 3ac - 6c + 5c - 3c - 24 + a^2 - 2c^2 = ac^2 - c^2

Simplifying further:
22a - 3ac - 4c - 24 + a^2 - 2c^2 = ac^2 - c^2

Therefore, (c+6)(3a-4) + (a-c)(1+c+a) - 3ac + 24 + 5c - 19a is equal to ac^2 - c^2.