Generally speaking, engineers operate by systematically describing a problem, the solutions’s requirements, and those requirements’ requirements until they get low enough level that they can identify a solution to a specific requirement, and then work back up to a solution.
Occasionally, an engineer will realize a better means of achieving some requirement or bypassing some problem and create a new solution based on their knowledge of science and math.
There can also be a large amount of Trial and Error involved as unexpected problems are revealed.
That’s as much as I can say without a specific example.
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