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The phrase "a very solid analysis" is correct and usable in written English.
You can use it when you want to express that an analysis is thorough, well-founded, and reliable.
Example: "After reviewing the report, I can confidently say that it provides a very solid analysis of the market trends."
Alternatives: "a robust analysis" or "a comprehensive analysis".
Exact(1)
The necessity of producing a very solid analysis has forced to limit the deflection of the jet in a very conservative range (±15°) with respect to the horizontal.
Similar(57)
Greg Laughlin, an astronomer at the University of California, Santa Cruz, and one of the few scientists who knew in advance of the paper, said, "It's a very solid dynamical analysis.
Successful applicants must have a very solid undergraduate background in mathematics, including at least real analysis, linear algebra, and ordinary differential equations (some exposure to partial differential equations is very desirable).
We need a very solid motive.
We played a very solid team game.
That's not a very solid foundation".
It has a very solid hook.
"It was a very solid diagnosis".
"It is a very solid performer".
"It was a very solid day.
The car has a very solid feel.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com