\[ k = 3(2)^2 - 12(2) + 7 = 12 - 24 + 7 = -5 \]

["Solving the Expression: Step-by-Step Calculation of ( k = 3(2)^2 - 12(2) + 7 )", "Understanding how to evaluate mathematical expressions is essential for mastering algebra. Today, we break down and solve the equation:", "[\nk = 3(2)^2 - 12(2) + 7\n]", "### Step 1: Evaluate the exponent\nThe expression begins with ( 3(2)^2 ). According to the order of operations (PEMDAS/BODMAS), exponents are calculated first.", "[\n(2)^2 = 4\n]\nSo,\n[\n3(2)^2 = 3 \ imes 4 = 12\n]", "### Step 2: Multiply the next term\nNext, we calculate ( -12(2) ):\n[\n-12 \ imes 2 = -24\n]", "### Step 3: Combine all terms\nNow substitute the results back into the original expression:\n[\nk = 12 - 24 + 7\n]", "### Step 4: Perform addition and subtraction from left to right\nFirst, subtract ( 24 ) from ( 12 ):\n[\n12 - 24 = -12\n]\nThen add ( 7 ):\n[\n-12 + 7 = -5\n]", "### Final Result\n[\nk = -5\n]", "---", "This stepwise breakdown not only ensures accuracy but also reinforces key algebraic rules—particularly the importance of exponents, multiplication, and the proper application of order of operations. Whether solving equations in homework or real-world applications, mastering these fundamentals empowers confident math problem-solving.", "Keywords: algebraic expression, solve for k, step-by-step math, exponent rules, order of operations, linear algebra problem, equation evaluation, mathematical calculation, validate algebra\nMeta Description: Follow a clear, step-by-step solution to evaluate ( k = 3(2)^2 - 12(2) + 7 ), showing each calculation from exponentiation to final result."]