`(2x - 3)/3 + (-3)/2 = (5 - 3x)/6 - 1/3`

`⇔ (2x - 3)/3 - (5 - 3x)/6 = 3/2 - 1/3`

`⇔ (2 ( 2x - 3 ))/6 - (5 - 3x)/6 = 7/6`

`⇔ 2 ( 2x - 3 ) : 6 - ( 5 - 3x ) : 6 = 7/6`

`⇔ ( 4x - 6 ) . 1/6 - ( 5 - 3x ) . 1/6 = 7/6`

`⇔ 1/6 . [ 4x - 6 - ( 5 - 3x )] = 7/6`

`⇔ 1/6 . ( 4x - 6 - 5 + 3x ) = 7/6`

`⇔ 1/6 . ( x - 11 ) = 7/6`

`⇔ x - 11 = 7/6 : 1/6`

`⇔ x - 11 = 7`

`⇔ x = 7 + 11`

`⇔ x = 18`

`----------------`

`a/b = a : b`