Photosynthesis-Equation
If you labeled the oxygen atoms in carbon dioxide in green and the oxgyen atoms in dioxygen in red (because they derived from photosynthesis, while $\ce{CO2}$ is used up in the Calvin cycle), you would have to add some water molecules to be able to write an equation like this:

$$\ce{6C\color{limegreen}{\ce{O2}} + 12H2\color{red}{\ce{O}} -&gt; C6H12\color{limegreen}{\ce{O6}} + 6\color{red}{\ce{O2}} + 6 H2\color{limegreen}{\ce{O}}}$$

This is problematic because oxygens in carbonyls can interchange with oxygens in water fairly rapidly (e.g. hydration of carbonyl to diol, and reverse reaction losing the "original" oxygen on the carbonyl). It would be fine to write the net reaction of the Calvin cycle separately from the net reaction of photosynthesis. This would also nicely show that hydrolysis of ATP is required for some of the steps, and that NADPH is involved.

On the other hand, if you are talking about the relationship between photosynthetic organisms vs other organisms, it is nice to have a simple net reaction for the entire organism (which also ignores that plant cells do break down glucose as well).


  Clearly there is much more going on as the formula most of us learned in school suggests, so my question is: what is the correct and complete equation for photosynthesis?


There is no official complete equation. You can add as much or as little detail you want. It really depends on where you want to go with the chemical equation. The links in the comments are great starting points.


  [OP, from comments:] Found the answer as to why i was confused by the simplified equation: "Hexose (six-carbon) sugars are not a product of the Calvin cycle. Although many texts list a product of photosynthesis as C6H12O6, this is mainly a convenience to counter the equation of respiration, where six-carbon sugars are oxidized in mitochondria. The carbohydrate products of the Calvin cycle are three-carbon sugar phosphate molecules, or "triose phosphates", namely, glyceraldehyde-3-phosphate (G3P)."


Great, it feels good to figure things out! In biochemical pathways, it can be difficult pinpointing products. The Calvin cycle and pentose phosphate pathway can be tweaked to make a variety of products, and those tweak affect what the "real" net reaction is.