Looks good to me.
Practice it more and the multiplying up stage will be a single line. You can just "see" that you get 16 on one side and 9x^2 on the other.
You could also go the crazy route and square-root the entire equation from step 1 to find that: 2/x = 3/2, so x = 4/3. Of course you lost the negative answer when taking the positive square root, so you know x = -4/3 is also a solution. But that's a bit mental and not advisable in an exam with ECFs.