Walkthroughs for custom maps.

Regarding cubic equations, I don't remember it being reduced to a quadratic equation; rather, I recall it being reduced to an equation of the form x^3 + px + q = 0.

Yes, a simple substitution is applied to this form, where x is replaced with the sum of two new unknowns, x = a + b.
In 2-3 lines and with one assumption, the equation is reduced to a quadratic equation. Solving it and returning to the original variables yields Cardano's formula.
In principle, knowing this first step (x = a + b) and understanding that it will lead to a quick solution allows you to guess what is done in those 2-3 lines.
However, guessing both the first step and everything else is a super-non-trivial task with a large number of possible substitutions. In fact, humanity has been working towards this for over a thousand years.
A similar situation exists here. In the battle with the champions, an unobvious simple first step is proposed, and knowing it allows you to guess the solution. Without knowing it, you can get lost in a multitude of options, which may not take thousands of years, but several years of mindless trial and error – and that's just for the first few moves.

The options against a single dragon are not tied to the landscape, and the dragon hardly interferes with the actions of other stacks. But here, the main idea of the battle is the 7 stacks of champions, which constantly interfere with each other and block each other – this is what generates a huge number of options, as well as where they will end up after their turn. They actively use wait, change the order of turns, choose top or bottom, and can change their trajectory due to the presence of a firewall, and sometimes paradoxically – the first stack without a firewall goes over the top, and after placing a wall in the middle, it happily changes its trajectory downwards to walk on it – like a child seeing a puddle.
And this directly depends on the location of the hexes with fake and firewall.

But, of course, knowing the solution, it is considered that the first move is obvious. Why look for a solution in other areas when you know where to look and that you will definitely find something there?
And other options for the first move, meanwhile, also have hints of a positive result. Oh yes, why look at them, intuition should have suggested that these are false hints. Bad intuition, you are punished, no ice cream for the rest of the month.
Or not false, has anyone studied all hundreds of thousands of variations of situations with 2 stacks of fake? Or have they? I'm just curious, what is the basis for the ironclad confidence that the solution should only be sought with such a first move (if you abstract and don't know about it)? Is it really obvious among all these options that the champions will always leave only one, and not two, hexes safe?
And yes, it is also so obvious that, having 140 mana for the next 4 battles, and constantly trying to minimize its consumption, that the first mana costs are not intended to deal damage.
I understand that it means tirelessly trying thousands of options that have a chance of leading to a solution for the first move, but if intuition fails and you come to the solution later rather than sooner, then are these just my problems? Interesting way to spend time, thank you. I appreciate this attitude.