To solve this equation, we need to follow the order of operations (PEMDAS - Parentheses, Exponents, Multiplication and Division, Addition and Subtraction):

Start by simplifying within the innermost parentheses:
(25x + 175) ÷ 6 + 58

Simplify the expression within the parentheses:
(25x + 175) ÷ 6 = 25x/6 + 175/6 = (25/6)x + 29.1667

Now, the expression becomes:
((25/6)x + 29.1667) + 58

Combine the two terms:
(25/6)x + 87.1667

Now, the expression becomes:
(25/6)x + 87.1667) ÷ 20 = 3

Solve for x:
(25/6)x = 3 - 87.1667
(25/6)x = -84.1667
x = (-84.1667 * 6) / 25
x = -20.50003

Therefore, the value of x that satisfies the equation is approximately -20.50003.