(5y-3)(3-y)-4(y-2)=3

Solution for (5y-3)(3-y)-4(y-2)=3 equation:

Simplifying
(5y + -3)(3 + -1y) + -4(y + -2) = 3

Reorder the terms:
(-3 + 5y)(3 + -1y) + -4(y + -2) = 3

Multiply (-3 + 5y) * (3 + -1y)
(-3(3 + -1y) + 5y * (3 + -1y)) + -4(y + -2) = 3
((3 * -3 + -1y * -3) + 5y * (3 + -1y)) + -4(y + -2) = 3
((-9 + 3y) + 5y * (3 + -1y)) + -4(y + -2) = 3
(-9 + 3y + (3 * 5y + -1y * 5y)) + -4(y + -2) = 3
(-9 + 3y + (15y + -5y2)) + -4(y + -2) = 3

Combine like terms: 3y + 15y = 18y
(-9 + 18y + -5y2) + -4(y + -2) = 3

Reorder the terms:
-9 + 18y + -5y2 + -4(-2 + y) = 3
-9 + 18y + -5y2 + (-2 * -4 + y * -4) = 3
-9 + 18y + -5y2 + (8 + -4y) = 3

Reorder the terms:
-9 + 8 + 18y + -4y + -5y2 = 3

Combine like terms: -9 + 8 = -1
-1 + 18y + -4y + -5y2 = 3

Combine like terms: 18y + -4y = 14y
-1 + 14y + -5y2 = 3

Solving
-1 + 14y + -5y2 = 3

Solving for variable 'y'.

Reorder the terms:
-1 + -3 + 14y + -5y2 = 3 + -3

Combine like terms: -1 + -3 = -4
-4 + 14y + -5y2 = 3 + -3

Combine like terms: 3 + -3 = 0
-4 + 14y + -5y2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
0.8 + -2.8y + y2 = 0

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + -2.8y + -0.8 + y2 = 0 + -0.8

Reorder the terms:
0.8 + -0.8 + -2.8y + y2 = 0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + -2.8y + y2 = 0 + -0.8
-2.8y + y2 = 0 + -0.8

Combine like terms: 0 + -0.8 = -0.8
-2.8y + y2 = -0.8

The y term is -2.8y.  Take half its coefficient (-1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
-2.8y + 1.96 + y2 = -0.8 + 1.96

Reorder the terms:
1.96 + -2.8y + y2 = -0.8 + 1.96

Combine like terms: -0.8 + 1.96 = 1.16
1.96 + -2.8y + y2 = 1.16

Factor a perfect square on the left side:
(y + -1.4)(y + -1.4) = 1.16

Calculate the square root of the right side: 1.077032961

Break this problem into two subproblems by setting 
(y + -1.4) equal to 1.077032961 and -1.077032961.

Subproblem 1
y + -1.4 = 1.077032961

Simplifying
y + -1.4 = 1.077032961

Reorder the terms:
-1.4 + y = 1.077032961

Solving
-1.4 + y = 1.077032961

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '1.4' to each side of the equation.
-1.4 + 1.4 + y = 1.077032961 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + y = 1.077032961 + 1.4
y = 1.077032961 + 1.4

Combine like terms: 1.077032961 + 1.4 = 2.477032961
y = 2.477032961

Simplifying
y = 2.477032961

Subproblem 2
y + -1.4 = -1.077032961

Simplifying
y + -1.4 = -1.077032961

Reorder the terms:
-1.4 + y = -1.077032961

Solving
-1.4 + y = -1.077032961

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '1.4' to each side of the equation.
-1.4 + 1.4 + y = -1.077032961 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + y = -1.077032961 + 1.4
y = -1.077032961 + 1.4

Combine like terms: -1.077032961 + 1.4 = 0.322967039
y = 0.322967039

Simplifying
y = 0.322967039

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.477032961, 0.322967039}