I wonder where you got the additional 2Y squared from at minute 2.53 - I still don't understand the multiplication of the first motif. I would have understood if you had said Y squared plus Y squared plus Y minus 1 equals zero, but why did you only multiply 2Y squared? It's not clear.
The question never said to only find the "real" solutions. Therefore, complex numbers with imaginary components should not be discarded as possible solutions.
5:00 you reject 16^x = -1 for having no real solutions but the original problem does not restrict solutions to reals.
With computers available this type of maths problems are best solved using numerical methods.
I wonder where you got the additional 2Y squared from at minute 2.53 - I still don't understand the multiplication of the first motif. I would have understood if you had said Y squared plus Y squared plus Y minus 1 equals zero, but why did you only multiply 2Y squared? It's not clear.
He is just writing the middle Y as (2Y-Y) to factor out common terms. Watch it once more.
The question never said to only find the "real" solutions. Therefore, complex numbers with imaginary components should not be discarded as possible solutions.