Is anything wrong about this phrase "We build software solutions designed for scalability"? I think there is, because the tenses are not consistent.
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There is absolutely nothing whatsoever wrong with that sentence. A participle that introduces a verbal phrase is under no obligation to agree with the tense of the main verb. That just would not be sensible.
Past participle used with non-past verbs:
Present participle used with non-present verbs:
Designed for scalability is a participle clause, postmodifying solutions. Designed is a non-finite verb, which means it shows no tense or person. The clause can be replaced with a finite relative clause with a passive verb: We build software solutions that are designed for scalability. That may help you understand why there is no inconsistency in the verbs.