To express \(3x^2 - 12x + 7\) in the form \(a(x + b)^2 + c\), follow these steps:

1. Factor out the coefficient of \(x^2\) from the quadratic and linear terms:

\(3(x^2 - 4x) + 7\)

2. Complete the square for the expression inside the parentheses:

\(x^2 - 4x = (x - 2)^2 - 4\)

3. Substitute back into the expression:

\(3((x - 2)^2 - 4) + 7\)

4. Distribute the 3 and simplify:

\(3(x - 2)^2 - 12 + 7\)

5. Combine the constants:

\(3(x - 2)^2 - 5\)

Thus, \(a = 3\), \(b = -2\), and \(c = -5\).