Question 1093850
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Introduce new variable  y = x-3  (the central point for the sequence x, x+2, x+4, x+6).


Then your equation takes the form

(y-3)*(y-1)*(y+1)*(y+3) = -16,   or

{{{(y^2-9)*(y^2-1)}}} = -16,

{{{y^4 - 10y^2 + 25}}} = 0,

{{{(y^2-5)^2}}} = 0,


which implies  {{{y^2}}} = 5,  and hence  y = +/- {{{sqrt(5)}}}.


<U>Answer</U>.  The original equation has the solutions  x = {{{3+sqrt(5)}}} and  {{{3-sqrt(5)}}}, each of multiplicity 2.
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<U>The lesson to learn from this solution</U>


<pre>
    The problem has a hidden symmetry around the central point.
    When written at variables centered at this point, the symmetry becomes explicit and facilitates the problem' solution.
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