2+2*(3+3*(4+4*x))=2012

To solve the equation \( 2 + 2 \cdot (3 + 3 \cdot (4 + 4x)) = 2012 \), we will simplify step by step.

1. Start by simplifying the expression inside the parentheses: \[ 4 + 4x \]

2. Now multiply this result by 3: \[ 3 \cdot (4 + 4x) = 12 + 12x \]

3. Next, substitute this back into the equation: \[ 2 + 2 \cdot (3 + (12 + 12x)) \]

4. Combine the terms inside the parentheses: \[ 3 + 12 + 12x = 15 + 12x \]

5. Now multiply by 2: \[ 2 \cdot (15 + 12x) = 30 + 24x \]

6. Now rewrite the entire equation: \[ 2 + 30 + 24x = 2012 \] \[ 32 + 24x = 2012 \]

7. Subtract 32 from both sides: \[ 24x = 2012 - 32 \] \[ 24x = 1980 \]

8. Now divide by 24: \[ x = \frac{1980}{24} \]

9. Simplify the fraction: \[ x = 82.5 \]

Thus, the solution to the equation is: \[ \boxed{82.5} \]