in Erwägung ziehen
to consider
To seriously consider something as a possibility or think about doing something.
Wir ziehen in Erwägung, nächstes Jahr ein Haus zu kaufen.
We are considering buying a house next year.

consideration
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to consider
To seriously consider something as a possibility or think about doing something.
Wir ziehen in Erwägung, nächstes Jahr ein Haus zu kaufen.
We are considering buying a house next year.

'Die Erwägung' (consideration) comes from the verb 'erwägen' (to consider). This verb contains the stem 'wägen', which means 'weigh'. So an 'Erwägung' is figuratively the weighing of reasons and possibilities, just as one compares weights on a scale.
Man muss die Vor- und Nachteile sorgfältig erwägen.
You have to carefully consider the pros and cons.
The word 'Erwägung' (consideration) belongs to formal language. You often find it in business, legal, or academic texts.
Aus finanziellen Erwägungen wurde das Projekt gestoppt.
The project was stopped for financial considerations.
The most common use is the fixed expression 'etwas in Erwägung ziehen' (to consider something). What you are considering can be a noun in the accusative or a subordinate clause, often an infinitive clause with 'zu'.
Ich ziehe einen Jobwechsel ernsthaft in Erwägung.
I am seriously considering changing jobs.
In the meaning of 'process of thinking', the word is often used in the fixed combination 'nach reiflicher Erwägung' (after careful consideration). This means 'after having thought about it long and thoroughly'.
Nach reiflicher Erwägung hat er sich für den anderen Kandidaten entschieden.
After careful consideration, he decided in favor of the other candidate.
When 'Erwägung' (consideration) means a single reason, it is often used in the plural with an adjective. Typical combinations are 'wirtschaftliche Erwägungen' (economic considerations), 'persönliche Erwägungen' (personal considerations), or 'strategische Erwägungen' (strategic considerations).
Bei der Entscheidung spielten vor allem persönliche Erwägungen eine Rolle.
Personal considerations played the main role in the decision.
reason / ground
'der Grund' and 'die Erwägung' can both play a role in a decision. 'der Grund' more often names the cause or reason: Why does someone do something? 'die Erwägung' more often means the process of thinking something over, or a point that you take into account when deciding. The word sounds somewhat more formal and often occurs in the plural: 'aus diesen Erwägungen' (for these considerations). Learners may confuse the words because a consideration can sometimes seem like a reason. Put simply: a reason explains the decision; a consideration is part of weighing things up before the decision.

Aus praktischen Erwägungen hat mein Nachbar den Termin auf den Nachmittag gelegt.
For practical considerations, my neighbor scheduled the appointment for the afternoon.
Wir hatten einen guten Grund, das teure Angebot abzulehnen.
We had a good reason to turn down the expensive offer.