Ako ovo rešenje ne bude dobro, tražićemo novo rešenje.

Because the sentence talks about a possible future situation.

• nije dobro = is not good now, in the present
• ne bude dobro = is not good / does not turn out good at that future point

After ako when Serbian refers to a future condition, it very often uses the form bude rather than a present-tense form like je.

So:

• Ako ovo rešenje nije dobro... = if this solution is not good (now)
• Ako ovo rešenje ne bude dobro... = if this solution is not good / does not prove good (when the time comes)

Bude is the special form of biti used in future-dependent clauses like this one.

In traditional grammar, this is treated as future II of biti. In practice, learners usually just need to remember:

• after ako
  • future meaning, Serbian often uses budem / budeš / bude / budemo / budete / budu

So Ako ovo rešenje ne bude dobro... is a very standard pattern.

Because Serbian future I can be formed with the auxiliary ću, ćeš, će, ćemo, ćete, će attached to the infinitive stem.

From tražiti:

• ja ću tražiti
• mi ćemo tražiti

But when the auxiliary comes after the infinitive stem, it combines into one word:

• tražićemo

So tražićemo means we will look for / we will seek.

A useful thing to remember:

• mi ćemo tražiti = also correct
• tražićemo = also correct
• tražiti ćemo = not standard

Because Serbian usually drops subject pronouns when they are not needed.

The ending -ćemo already tells you the subject is we.

So:

• tražićemo = we will seek
• mi tražićemo would sound unnecessary in normal speech
• mi ćemo tražiti is possible if you want emphasis or contrast

They agree with rešenje, which is a neuter singular noun.

So the forms are:

• ovo rešenje = this solution
• novo rešenje = new solution

Serbian adjectives and demonstratives must agree with the noun in:

• gender
• number
• case

Since rešenje is neuter singular, you get ovo and novo.

It is not the same grammatical function in both places, even though the form looks the same.

1. ovo rešenje
   Here rešenje is the subject, so it is in the nominative.

2. novo rešenje
   Here rešenje is the direct object of tražićemo, so it is in the accusative.

Why do they look identical? Because for many neuter singular inanimate nouns, nominative and accusative have the same form.

Here it is functioning as a predicate adjective, agreeing with rešenje.

Because rešenje is neuter singular, the matching form is dobro.

So in this sentence:

• rešenje je dobro = the solution is good

It looks identical to the adverb dobro meaning well, but here it is not an adverb like in:

• On radi dobro = He works well

Ako means if and introduces the condition.

The structure is:

• Ako
  • condition
• result clause

So:

• Ako ovo rešenje ne bude dobro = if this solution is not good
• tražićemo novo rešenje = we will look for a new solution

This is a very common Serbian pattern for real or possible future conditions.

Yes, Serbian word order is fairly flexible, but the given sentence is the most neutral and natural version.

Standard order here:

• Ako ovo rešenje ne bude dobro, tražićemo novo rešenje.

You could change it for emphasis, for example:

• Ako ovo rešenje ne bude dobro, novo rešenje ćemo tražiti.

That puts extra focus on novo rešenje, but it sounds more marked.

So for learners, the original word order is the best one to remember first.

Because in Serbian, ne is usually written separately from the verb.

So:

• ne bude
• ne tražimo
• ne radi

There are some common exceptions, such as:

• nisam
• nemam
• neću

But with bude, the correct spelling is ne bude.

Tražiti is imperfective and gives a neutral meaning: we will look for / seek a new solution.

A perfective form like potražiti would add a slightly different nuance, more like:

• we’ll go look for
• we’ll make an attempt to find

So:

• tražićemo novo rešenje = neutral, general
• potražićemo novo rešenje = a bit more bounded, one concrete attempt/action

In this sentence, tražićemo is very natural.

Yes, but the meaning shifts a little.

• Ako ovo rešenje nije dobro... focuses more on the solution’s present quality: if this solution is not good
• Ako ovo rešenje ne bude dobro... sounds more like a future test or future outcome: if this solution turns out not to be good

So both are possible in the right context, but the original sentence is better if you mean a future, still-uncertain result.