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 + 4428y - 7y = 44 - 1021y = 34y = 34/21y = 1.619
Therefore, the solution to the equation is y = 1.619.
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.