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The equation '3x=9' is a simple linear equation with one unknown. To solve it, one can divide both sides of the equation by 3, resulting in x=3. Factorizing '3x-9' involves identifying common factors, here being 3, thus it can be written as 3(x-3). Solving the equation '3x-9=12' step-by-step involves first adding 9 to both sides to get '3x=21', then dividing both sides by 3 to find 'x=7'. These operations are fundamental in algebra and commonly used in solving linear equations.

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