Factorials of the Plane!

Calculus Level 1

Let xx be a real number satisfying x!+(x1)!=3x(x1)!x! + (x-1)! = 3x(x-1)!, find the value of 4x4x.

To clarify, x!=Γ(x+1)x! = \Gamma(x + 1) , where Γ()\Gamma(\cdot) denotes the gamma function. In other words, even if xx is not an integer, x!x! can be computed.

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