Transforming CoefficitenList[] output into set of equations to use in Solve[]

Questions
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1

How do I transform the result of CoefficientList[] into a set of equations, which I can solve for example with Solve[]. See attached file for the following example.

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Post_20241228.nb (115 KB)

2

Hi Guido! Try taking the dot product with the corresponding variable powers list:

CoefficientList[1 + 6 x - x^4, x]

gives

{1, 6, 0, 0, -1}

and

{1, 6, 0, 0, -1} . Array[x^(#-1)&, 5]

or

{1, 6, 0, 0, -1} . Table[x^n, {n,0,4}]

gives

1 + 6 x - x^4

back.