We have,
22x+2−6x−2.32x+2=0
now,
⇒22(x+1)−6x−2.32(x+1)=0
⇒4(x+1)−6x−2.9(x+1)=0
⇒4x.4−2x.3x−2.(9x.9)=0
⇒4.(2x)2−2x.3x−18(3x2)=0
on divide (2x2) and we get,
⇒4.(2x)2(2x)2−2x.3x(2x)2−18[(32)x]2=0
⇒4−(32)x−18[(32)x]2=0
let, (32)x=y−−−−(1)
now,
⇒4−y−18y2=0
on factorize
⇒4−(9−8)y−18y2=0
⇒4−9y+8y−18y2=0
⇒1(4−9y)+2y(4−9y)=0
⇒(4−9y)(1+2y)=0
⇒4−9y=0,1+2y=0
⇒y=49→ (choose), y=−12 (not choose)
using equation (1)
(32)x=49
⇒(32)x=(23)2
on reciprocal
⇒(32)x=(32)−2
then, comparing,
x=−2
Hence, this is the answer.