To solve this equation, we need to follow the order of operations (PEMDAS/BODMAS).

First, let's simplify the expression inside the innermost parentheses:

(4x + 28) ÷ 3 + 55 = 35

Next, let's simplify the division:

(4x + 28) ÷ 3 + 55 = 35
(4x + 28) ÷ 3 = 35 - 55

Now, let's simplify the subtraction:

(4x + 28) ÷ 3 = -20

Next, let's multiply both sides of the equation by 3 to eliminate the division:

(4x + 28) = -20 * 3

Now, let's simplify the multiplication:

4x + 28 = -60

Next, let's subtract 28 from both sides of the equation:

4x = -60 - 28

Now, let's simplify the subtraction:

4x = -88

Finally, let's divide both sides of the equation by 4 to solve for x:

x = -88/4

Now, let's simplify the division:

x = -22

Therefore, the solution to the equation is x = -22.