If the number is x, (3x-5)(4x-1)=7. Without making this into a quadratic, we know the factors of 7 are 1 and 7, so either 4x-1=1 or 7. If 4x-1=7, 4x=8 and x=2. 3x-5=6-5=1, therefore x=2 is a solution.
Now quadratically: 12x^2-23x+5-7=12x^2-23x-2=0=(x-2)(12x+1). There are two solutions, x=2 and x=-1/12.