Expanding the left side of the equation:

(6y+2)(5-y)
= 6y(5-y) + 2(5-y)
= 30y - 6y^2 + 10 - 2y
= -6y^2 + 28y + 10

Expanding the right side of the equation:

47 - (2y-3)(3y-1)
= 47 - (6y^2 - 2y + 9y - 3)
= 47 - 6y^2 + 7y - 3
= -6y^2 + 7y + 44

Now, the equation becomes:

-6y^2 + 28y + 10 = -6y^2 + 7y + 44

Subtracting -6y^2 from both sides and rearranging the equation:

28y + 10 = 7y + 44
28y - 7y = 44 - 10
21y = 34
y = 34/21
y = 1.619

Therefore, the solution to the equation is y = 1.619.