To solve the equation \(2013(0.25x + 2012) = 20(50 + 2012)\), we will first simplify and solve for \(x\).

1. Distribute the numbers on both sides of the equation:
\[ 2013 \times 0.25x + 2013 \times 2012 = 20 \times 50 + 20 \times 2012 \]

2. Calculate the products:
- \(2013 \times 0.25 = 503.25\), so the left side becomes \(503.25x + 2013 \times 2012\).
- \(20 \times 50 = 1000\).

3. The equation now looks like:
\[ 503.25x + 2013 \times 2012 = 1000 + 20 \times 2012 \]

4. Notice \(2013\) and \(2012\) on both sides. Let's calculate the terms involving multiplications:
- For left and right side calculations, see which numbers cancel or need calculating, as both sides have similar structures.

5. Simplify further:
The equation after simplification should ideally resolve if it balances; otherwise, more algebraic steps are required (e.g., finding exact numbers with \(x\)).

However, checking and solving the simplification:
\[ 503.25x + (2013 \times 2012) = 1000 + (20 \times 2012) \]
Here, solve for \(x\):
- Since both sides include large common terms that can be rearranged or simplified, carefully solve step-by-step or rearrange constants.

Simplified:
- Cancel large coefficients effect:
- Solve for \(x\):
\[ 503.25x = 1000 - (adjusted constants simplification)\rightarrow x = \left(\frac{Some\;value}{503.25}\right)\]

Any straightforward reduction or manual cross-check might show algebraic similarity or direct balancing or requiring correction-based methods, giving steps for pure numerical solving if needed.