Mathematical Simplification Solution

This solution details the step-by-step simplification of the given mathematical expression using the standard order of operations (PEMDAS/BODMAS).

Step-by-Step Simplification Process

1. Simplify the first major term: $[(36 + 4 \times (3 + 2 \times (5 - 2))) \div (6 + 3)]$
   • Evaluate the innermost parentheses: $5 - 2 = 3$.
   • Evaluate the next level of parentheses: $3 + (2 \times 3) = 3 + 6 = 9$.
   • Evaluate the expression within the square brackets' first part: $36 + (4 \times 9) = 36 + 36 = 72$.
   • Evaluate the denominator: $6 + 3 = 9$.
   • Calculate the value of the first major term: $72 \div 9 = 8$.
2. Simplify the second major term: $[(40 - (6 + 3 \times 2)) + (8 \times 2 - 6)]$
   • Evaluate the inner parentheses: $6 + (3 \times 2) = 6 + 6 = 12$.
   • Calculate the first part of the second term: $40 - 12 = 28$.
   • Calculate the second part of the second term: $(8 \times 2) - 6 = 16 - 6 = 10$.
   • Calculate the value of the second major term: $28 + 10 = 38$.
3. Combine the results: Add the values obtained from the two major terms.
   • Final calculation: $8 + 38 = 46$.

Final Simplified Value

The simplified value of the expression $[(36 + 4 \times (3 + 2 \times (5 - 2))) \div (6 + 3)] + [(40 - (6 + 3 \times 2)) + (8 \times 2 - 6)]$ is 46.