Find all solutions (answers should be given in simplified form). Some answers may involve the number i.

Question

(x^2/6) - (2x/3) = 3 + (x/2)

I turned (2x/3) into (4x/6) and subtracted it from (x^2/6) to get: x(x-4) / 6

I turned 3 into 6/2 and added it to (x/2) to get: (x+6) / 2

So that leaves me with:
x(x-4) / 6 = (x+6)/6

Where do I go from here?

Answer 1

Sorry, the final line should read:

x(x-4) / 6 = (x+6)/2

Answer 2

I think what "you do from here" is to expand and factor the terms; however, can you subtract 2x/3 from X^2/6. Those are not like terms. I don't believe you can do that, at least not legally. Therefore, I don't agree with the "getting here" part.

Consider using the original equation, multiplying everything by 6 (to clear the denominators), factor the terms and sove the equation. See if that doesn't give you x = -2 and x = +9. Then substitute those numbers into the original equation and see if the equation is satisfied.