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To solve the equation \( 36x^2 = 0 \), we first divide both sides by 36, which simplifies to:
\[
x^2 = 0
\]
Taking the square root of both sides, we find:
\[
x = 0
\]
Thus, the solution set contains only the value 0. In set notation, this is represented as:
\[
\{0\}
\]
So, the correct response is:
\(\{0\}\)