Solving $0=sum_{T=0}^{L}(2u^2A-2Ou)$ for $O$

Mathematics Asked on January 1, 2022

I know this seems like a very simple question, but I haven’t been able to find anything online regarding the answer to this.

Even WolframAlpha, which I usually use when I don’t know the answer to a problem like this, fails to find a result.

I need to rearrange for O (and then fully simplify): $$0=sum_{T=0}^{L}(2u^2A-2Ou)$$

Where $u$ is an expression that includes $T$, and $A,O, L$ are all variables

So far, my working includes:





If this is all correct, can this final expression of $frac{Asum_{T=0}^{L}(u^2)}{sum_{T=0}^{L}(u)}$ be simplified further?

Simplifying to $Asum_{T=0}^{L}(u)$ doesn’t seem to work

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