11(y-1)(3-y)=2y

Solution for 11(y-1)(3-y)=2y equation:

Simplifying
11(y + -1)(3 + -1y) = 2y

Reorder the terms:
11(-1 + y)(3 + -1y) = 2y

Multiply (-1 + y) * (3 + -1y)
11(-1(3 + -1y) + y(3 + -1y)) = 2y
11((3 * -1 + -1y * -1) + y(3 + -1y)) = 2y
11((-3 + 1y) + y(3 + -1y)) = 2y
11(-3 + 1y + (3 * y + -1y * y)) = 2y
11(-3 + 1y + (3y + -1y2)) = 2y

Combine like terms: 1y + 3y = 4y
11(-3 + 4y + -1y2) = 2y
(-3 * 11 + 4y * 11 + -1y2 * 11) = 2y
(-33 + 44y + -11y2) = 2y

Solving
-33 + 44y + -11y2 = 2y

Solving for variable 'y'.

Reorder the terms:
-33 + 44y + -2y + -11y2 = 2y + -2y

Combine like terms: 44y + -2y = 42y
-33 + 42y + -11y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
-33 + 42y + -11y2 = 0

Begin completing the square.  Divide all terms by
-11 the coefficient of the squared term: 

Divide each side by '-11'.
3 + -3.818181818y + y2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -3.818181818y + -3 + y2 = 0 + -3

Reorder the terms:
3 + -3 + -3.818181818y + y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -3.818181818y + y2 = 0 + -3
-3.818181818y + y2 = 0 + -3

Combine like terms: 0 + -3 = -3
-3.818181818y + y2 = -3

The y term is -3.818181818y.  Take half its coefficient (-1.909090909).
Square it (3.644628099) and add it to both sides.

Add '3.644628099' to each side of the equation.
-3.818181818y + 3.644628099 + y2 = -3 + 3.644628099

Reorder the terms:
3.644628099 + -3.818181818y + y2 = -3 + 3.644628099

Combine like terms: -3 + 3.644628099 = 0.644628099
3.644628099 + -3.818181818y + y2 = 0.644628099

Factor a perfect square on the left side:
(y + -1.909090909)(y + -1.909090909) = 0.644628099

Calculate the square root of the right side: 0.802887351

Break this problem into two subproblems by setting 
(y + -1.909090909) equal to 0.802887351 and -0.802887351.

Subproblem 1
y + -1.909090909 = 0.802887351

Simplifying
y + -1.909090909 = 0.802887351

Reorder the terms:
-1.909090909 + y = 0.802887351

Solving
-1.909090909 + y = 0.802887351

Solving for variable 'y'.

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

Add '1.909090909' to each side of the equation.
-1.909090909 + 1.909090909 + y = 0.802887351 + 1.909090909

Combine like terms: -1.909090909 + 1.909090909 = 0.000000000
0.000000000 + y = 0.802887351 + 1.909090909
y = 0.802887351 + 1.909090909

Combine like terms: 0.802887351 + 1.909090909 = 2.71197826
y = 2.71197826

Simplifying
y = 2.71197826

Subproblem 2
y + -1.909090909 = -0.802887351

Simplifying
y + -1.909090909 = -0.802887351

Reorder the terms:
-1.909090909 + y = -0.802887351

Solving
-1.909090909 + y = -0.802887351

Solving for variable 'y'.

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

Add '1.909090909' to each side of the equation.
-1.909090909 + 1.909090909 + y = -0.802887351 + 1.909090909

Combine like terms: -1.909090909 + 1.909090909 = 0.000000000
0.000000000 + y = -0.802887351 + 1.909090909
y = -0.802887351 + 1.909090909

Combine like terms: -0.802887351 + 1.909090909 = 1.106203558
y = 1.106203558

Simplifying
y = 1.106203558

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.71197826, 1.106203558}