1) (x+1)(x+2) = (x-3)(x+4)
x^2 + 3x + 2 = x^2 + x - 12
3x + 2 = x - 12
2x = -14
x = -7

2) (3x-2)(2x+7) - (x+1)(6x-5) = 16
6x^2 + 21x - 4x - 14 - 6x^2 + 5x + 6x - 5 = 16
22x - 19 = 16
22x = 35
x = 35/22 or x = 1.59

3) 24 - (3y+1)(4y-5) = (11-6y)(2y-1) + 6
24 - 12y^2 + 19y - 5 = 22y^2 - 11y - 6 + 6
24 - 12y^2 + 19y - 5 = 22y^2 - 11y
12y^2 - 19y + 5 = 22y^2 - 11y
0 = 10y^2 - 8y - 5
y = (-(-8) ± √((-8)^2 - 410(-5))) / 2*10
y = (8 ± √(64 + 200)) / 20
y = (8 ± √264) / 20
y = (8 ± 2√66) / 20
y = (4 ± √66) / 10

4) (6y + 2)(5-y) = 47 - (2y-3)(2y-1)
(6y + 2)(5 - y) = 47 - (2y-3)(2y-1)
30y - 6y^2 + 10 - 2y = 47 - 4y^2 + 5y + 6
-6y^2 + 30y + 10 - 2y = 47 - 4y^2 + 5y + 6
-4y^2 + 28y + 4 = 47 - 4y^2 + 5y
28y + 4 = 47 + 5y
23y = 43
y = 43/23 or y = 1.87