Let's first simplify the left side of the equation:

(x+3)(x+7) - x(x+8)
(x^2 + 7x + 3x + 21) - (x^2 + 8x)
(x^2 + 10x + 21) - (x^2 + 8x)
x^2 + 10x + 21 - x^2 - 8x
2x + 21 - 8x
-6x + 21

Now we have the equation: -6x + 21 = 16

To solve for x, we can move the 21 to the other side by subtracting 21 from both sides:

-6x = 16 - 21
-6x = -5

Finally, divide by -6 to solve for x:

x = -5 / -6
x = 5/6

Therefore, the solution to the equation is x = 5/6.