Connection between saving and investments-Y=C+I+G+NX I understand
Y-G-C = I+NX = Savings . The equation that we see everywhere in economic textbooks. I see the mathematical logic.
BUT
Given that I = capital investment in GDP accounting surely Savings are what is not spent after you haven't spent anything on capital goods etc. So in my head
Y-G-C-I = NX = S and infact why not take NX over to the other side!
What &quot;mistake&quot; am I making here?
I can regurgitate the textbooks and get the marks but I just don't understand it for myself from first principles.
The $I$ is actually not just capital spending. In some models that might be true, for example, in Solow growth model we will assume that all investment is capital spending but $I$ is not just that.
For example, $I$ would include both purchases of new houses (although argument could be made they are capital goods, they would not satisfy more narrower definitions requiring that capital being factor of production), or investment in inventory for example (see more detailed explanation in Blanchard et al. Macroeconomics: a European Perspective, pp 41-43).
Also, spending on capital good is literary considered saving in economics. In economics saving has more broad meaning than what ordinary people just consider 'saving'. For example, in economics when you buy stocks you are also saving even if you spend money doing so.  In economics by definition the portion of income that is not consumed is saving (see ibid. Macroeconomics: a European Perspective pp 569-570).
PS: As pointed in the comments, you should have minus in front of $C$ so the equation should be: $ Y-G-C = I+NX$.