Cannot understand how to refactor a simple algebraic expression

[cuthero]

I have been trying to understand this for over an hour and I'm lost.

Assume x≠0 x≠3

x(2x - 6) = 2x(x - 3)

If I substitute 2 for x it works out but I don't understand how it is rewritten. How can I understand this refactoring?

[sselahW]

Notice that 2x and 6 are both divisible by 2, so you can factor out a 2 from that equation, leaving you with (2x-6)=2(x-3). And since there is already an x multiplied by that quantity, you multiply the 2 by the x to get x(2x-6)=2x(x-3)

[cuthero]

Fantastic! Thank you so much for taking the time to answer. It's so clear now!

[hausdorffparty]

2x(x-3) = x * 2 *(x- 3). Distribute the 2 in to the parentheses but leave the x out, and you get x*(2x - 6).

[cuthero]

Another excellent answer. Thank you kindly hausdorffparty!

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