左右する【さゆうする】

左右する means "to decide", "to have a decisive effect on": the cause takes が and what it affects takes を. 左右 is "left and right", and the idea is that A can swing B one way or the other.

The effect is large. For a small influence, えいきょう影響する or えいきょう影響をあたえる与える fits better. おおきく大きく often goes in front: おおきく大きくさゆう左右する.

左右される

In the passive, the thing affected is the subject, and the cause takes に: "to be swayed by", "to depend on". Said of a person, it means letting something outside push you around.

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左右する is a written word, at home in news, essays and business reports. In conversation, "it depends on X" is usually きごう〜しだい次第だ or きごう〜できまる決まる.