Solve for variable

[limpid crest]

I honestly haven't even tried solving it yet, but it doesn't look like something you can just finish out of nowhere

[final harness]

First notice that there is a c^4, c^8, c^12, which are equal to c^4, (c^4)^2, (c^4)^3, so you could substitute something in like x= c^4 and then solve for x.

So it simplifies to 4x^3 + (4y^2 - 4)x^2 - (4z^2)x - z^4 = 0

So it is just a cubic equation.

There is a formula for this.

It might be easier if you could factor a factor out.

[limpid crest]

Oh I actually know that one by heart

√((-b³/27a³+bc/6a²-d/2a)+³√((-b³/27a³+bc/6a²-d/2a)²+(c/3a-b²/9a²)³) v √((-b³/27a³+bc/6a²-d/2a)-³√((-b³/27a³+bc/6a²-d/2a)²+(c/3a-b²/9a²)³)-b/3a

Thanks