To solve the expression \(3 \cdot 6 + 9 \cdot 2 - (2 \cdot 7 + 12 \div 6 \cdot 5)\), we need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right), often abbreviated as PEMDAS.
Let’s break it down step-by-step:
Calculate the expressions inside the parentheses first:
- Inside the parentheses: \(2 \cdot 7 = 14\)
- Then calculate \(12 \div 6 = 2\)
- Now we have \(2 \cdot 5 = 10\)
- So the expression in parentheses becomes \(14 + 10 = 24\).
Now we evaluate the rest of the expression:
- Calculate \(3 \cdot 6 = 18\)
- Calculate \(9 \cdot 2 = 18\)
Now substitute these results into the expression: \[ 18 + 18 - 24 \]
Now perform the addition and subtraction from left to right:
- \(18 + 18 = 36\)
- \(36 - 24 = 12\)
Therefore, the final result of the expression \(3 \cdot 6 + 9 \cdot 2 - (2 \cdot 7 + 12 \div 6 \cdot 5)\) is
\[ \boxed{12} \]