To solve the equation 4x + 7 = -28 - x:

First, combine like terms on both sides of the equation:
4x + x = -28 - 7
5x = -35

Next, divide by 5 on both sides to isolate x:
x = -35/5
x = -7

Therefore, the solution to the equation 4x + 7 = -28 - x is x = -7.

Next, to solve the equation 2(3-4x) - 5 = 6 - 7(x+8):

First, distribute the 2 on the left side and distribute the -7 on the right side:
6 - 8x - 5 = 6 - 7x - 56

Combine like terms:
-8x + 1 = -7x - 50

Subtract -7x from both sides:
-x + 1 = -50

Subtract 1 from both sides:
-x = -51

Divide by -1 to isolate x:
x = 51

Therefore, the solution to the equation 2(3-4x) - 5 = 6 - 7(x+8) is x = 51.