1) (x+1)(x+2)=(x-3)(x+4)
x^2+2x+x+2=x^2+4x-3x-12
x^2-x^2+3x-x=-14
2x=-14
x=-7
2) (3x-1)(2x+7)-(x+1)(6x-5)=16
6x^2+21x-2x-7-(6x^2-5x+6x-5)=16
6x^2+21x-2x-6x^2+5x-6x=16+7-5
18x=18
x=1
3) 24-(3y+1)(4y-5)=(11-6y)(2y-1)+6
24-(12y^2-15y+4y-5)=22y-11-12y^2+6y+6
24-12y^2+11y+5=28y-5-12y^2
-12y^2+11y-28y+12y^2=-5-24-5
-17y=-34
y=2
4) (6y+2)(5-y)=47-(2y-3)(3y-1)
30y-6y^2+10-2y=47-(6y^2-2y-9y+3)
28y-6y^2=47-6y^2+11y-3-10
28y-6y^2+6y^2-11y=47-3-10
17y=34
y=2