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coercion into series

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I encountered the following commands

 Solve[(y + b) (y + c) == (a^4 + y^2 + 3) + O[y]^3, {b, c}]
 Solve[(a^2 + a c + b)(a^2 + a e + d) == (a^4 + y^2 + 3) + O[a]^5, {b,
c, d, e}]

I can't find anywhere documentation for this setting of Solve.
In what technique is based this solution?

Thanks a lot.

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