Collapse a Sum / factor an element out of a sum

Question

I am trying to get something in the form of a $\Sigma (\dots) * \alpha_i = (\dots)$ from the output of the code below. The thing is that I cannot figure out how to tell Mathematica to "collapse" down to a single sum and factor out the $\alpha_i$.

Thank you,

John

$Assumptions = 
i \[Element] Integers && j \[Element] Integers && 
n \[Element] Integers && i \[Element] Constant && 
j \[Element] Constant && n \[Element] Constant;

r[t_] = (D[#, {t, 2}] - t*D[#, t] + 1/6*# - (-3)) &;
inner[x_] = (Integrate[
 Simplify[
  ComplexExpand[#1 Conjugate[#2], 
   TargetFunctions -> {Re, Im}]], {x, 0, 10}]) &;

uB = 5 - \[Pi]/5*x;
\[Phi][i_] = x^i*(10 - x);
uApp = uB + Sum[Subscript[\[Alpha], i]*\[Phi][i], {i, 1, n}];

(r[x][uApp] /. x -> (10 - 0)/(n + 1)*j) == 0