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

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

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