@C_R Please don't spawn a wholly separate new Question thread on the issue of what your sheet looks like in M2015.

@Michael If you know that you only need to deal with a single factor then you could avoid the unnecessary expense of a complete factorization (eg. using ifactors) and just do divisions.

I would have suggested this earlier but the OP didn't originally give such details of the goal.

Please put close followups on your underlying problem in this (or one of your related previous Question threads), instead of spawning whooly new and separate Question threads for your problem.

@nicolesharp100 Please do not post a duplicate of this in an alternate Mapleprimes forum.

Feel free to submit an SCR (software change request).

@Linhuchong As Tom mentioned, there are several ways. I like his use of geometry.

I also like vv's approach.

For fun, keeping with implicitplot for no particular reason (and now more clumsily calling solve twice),

restart;
f:=2.96736996560705*10^(-12)*p^2+1.31319840299485*10^(-13)*t^2
   -8.89549693662593*10^(-7)*p+8.53128393394231*10^(-7)*t
   -3.65558815509970*10^(-30)*p*t-1:
P:=remove(has,solve(f<0,[p,t])[],t);
T:=remove(has,solve(f<0,[t,p])[],p);
p1,p2:=rhs(P[1]),lhs(P[2]);
t1,t2:=rhs(T[1]),lhs(T[2]);
plots:-implicitplot(f,p=p1..p2,t=t1..t2,scaling=constrained);

@Bennyjay You're welcome. We all make mistakes now and then.

By the way, if you're looking for a solution with all values nonnegative,

eqs := {Why, Do, It, Today, When, Its, Due, Tomorrow}:
vars := indets({Why, Do, It, Today, When, Its, Due, Tomorrow},name):
solve(eqs union (vars>=~0));

   {Cl = .8562628337e-2, H = .6579879116e-8, H2PO4 = .9122851784e-3,
    H3PO4 = .7913134254e-9, HPO4 = .8548948565e-2, Na = .2657618944e-1,
    OH = .1519784760e-5, PO4 = .6218631025e-6}

@FDS You are welcome. There's no reason to apologize, and I don't think that is was a basic query. The file is unusual.

@FDS The code that I provided works fine for me, even if the original input file has no filename extension.

As far as I can see, your issue isn't caused by the filename extension (or lack of it). Rather, it's caused by having all the text characters in your input file be separated by null characters, which may confuse some import mechanisms. I show a way to remove them. There are other ways.

(In contrast, your older Question thread had an example in which every character was separated by a space, which is different.)

The initial commands below import the data from the extensionless file, get rid of the null separators, and then write out the remaining content to a new plaintext file which can be imported in usual ways.

For example,

restart;
interface(rtablesize=100):

U:=FileTools:-Binary:-ReadFile("Spiking2011622"):
Q:=Array(remove(type,convert(U,list),0),datatype = integer[1]):
FileTools:-Binary:-WriteFile("Spiking2011622Q.txt",Q):

M:=ImportMatrix("Spiking2011622Q.txt"):

# And now the Matrix may be split by groups of rows,
# at the headers.
L:=[ListTools:-SearchAll("Id",convert(M[..,1],list))];
numelems(L);
All:=[seq(M[L[i]..L[i+1]-1,..],i=1..nops(L)-1)]:
map(numelems,All);
All[5][1..10,..], All[16][1..11,..];
All[5][11..,..], All[16][12..,..];

I have submitted a bug report.

A shorter example that fails the first time, in my Maple 2023.0:

restart;
expr := (x^2)^(1/2)/((x+y)*sqrt(x^2+1)+x^2*(1/2*y^2-1))^2:

simplify(expr);
Error, (in simplify/size/collect_and_recurse) invalid arguments to coeffs

In my Maple 2022.2 (64bit Linux) this example and the OP's worksheet run without error.

@MDD You could create a re-usable procedure (to handle the entries individually, via map, or which itself maps across F).

Such a procedure could accept a list of names, L, so that the sort could be done with plex(op(L)).

Let me know if you'd like the whole thing shown.

@C_R Why do you write it as , "new options" in the context of your example? Your smaller example works in many older versions.

How would you use your suggestion of convert (sincos and/or tan, etc) to handle the OP's original example to get a form as he expected?

@C_R I meant what I wrote in the first snippet, addressing the OP's actual example and literal query about cot(90 - alpha/2).

I wrote only the second snippet because I wasn't sure whether the "-90" was intentional (in radians).

@MANUTTM Why didn't you mention this goal at the beginning?

Why do you keep starting separate Question threads on the same underlying problem?

@MANUTTM I don't know what accuracy you'll be needing, both for the estimated roots as well as following substitution of such solutions into other expressions (or the original equation). You might need to adjust the working precision according to what you later do with the computed roots.

If you substitute values for i into K2 then its values may become very large (positive or negative) if you allow a wide a range for t2. And (as a function of t2) it can be very steep near the root, relative to when t2 is far from the root, which can make the numeric root-finding more difficult. By using a restricted range for t2 the root-finding process can do better.