To simplify the expression \((3+i)[(2−i)+(3i−4)]\), we first simplify the inner expression \((2−i)+(3i−4)\):
\[ (2 - i) + (3i - 4) = 2 - 4 + (-i + 3i) \]
Now, we combine the real and imaginary parts:
\[ = (2 - 4) + (-i + 3i) = -2 + 2i \]
Next, we substitute this back into the original expression:
\[ (3+i)[-2 + 2i] \]
Now we will use the distributive property to expand:
\[ = 3(-2) + 3(2i) + i(-2) + i(2i) \]
Calculating each term gives us:
\[ = -6 + 6i - 2i + 2i^2 \]
We know that \(i^2 = -1\), so we substitute:
\[ = -6 + 6i - 2i + 2(-1) \]
This simplifies to:
\[ = -6 - 2 + 6i - 2i \]
Combining like terms, we have:
\[ = -8 + 4i \]
Thus, the simplified expression is:
\[ \boxed{-8 + 4i} \]