The function $f(x)$ satisfies
\[f(x) + f(2x) + f(2 - x) + f(x + 1) = x\]for all real numbers $x.$  Find $f(0).$
Question:
The function $f(x)$ satisfies
\[f(x) + f(2x) + f(2 - x) + f(x + 1) = x\]for all real numbers $x.$  Find $f(0).$
Answer:
Let's think step by step.

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The function $f(x)$ satisfies
\[f(x) + f(2x) + f(2 - x) + f(x + 1) = x\]for all real numbers $x.$  Find $f(0).$
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