He started with 2*x² then he somehow got 2*2*x

From my percepective, he's trying to solve it by changing x² to 2x.

x² =/= 2x

if x=6,

x² 2x
= 6² = 2*6
= 6*6 = 12
= 36

36 =/= 12

2*2*x is only true when x=2

Let's say x=5,

2*x²
= 2*5²
= 2*5*5
= 2*25
= 50

Following your logic, 4*x = 50

4*5
= 20
20 =/= 50
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4*x = 2*x²
÷2 ÷2
= 2*2 = x²
= 2*2 = x²
= 4 =x²
=√4 = √x²
= 2 = x

The equation 4x is only valid if x=2.
xЄ = [2]