To factorize the expression 9x^2 + 4y^2 + z^2 - 12xy + 4yz - 6xz quickly, we can use grouping and rearrange the terms:
(9x^2 - 12xy - 6xz) + (4y^2 + 4yz) + z^2
Now, let's factor each grouped term separately:
Factor out 3x from the first group: 3x(3x - 4y - 2z)
Factor out 4y from the second group: 4y(y + z)
The third group, z^2, cannot be factored any further.
Putting it all together, we have the factored form:
3x(3x - 4y - 2z) + 4y(y + z) + z^2
Please note that this is the simplified form of the expression, but it may not necessarily be further factorizable.