5y(11-2y)=3

Solution for 5y(11-2y)=3 equation:

Simplifying
5y(11 + -2y) = 3
(11 * 5y + -2y * 5y) = 3
(55y + -10y2) = 3

Solving
55y + -10y2 = 3

Solving for variable 'y'.

Reorder the terms:
-3 + 55y + -10y2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 55y + -10y2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
0.3 + -5.5y + y2 = 0.0

Move the constant term to the right:

Add '-0.3' to each side of the equation.
0.3 + -5.5y + -0.3 + y2 = 0.0 + -0.3

Reorder the terms:
0.3 + -0.3 + -5.5y + y2 = 0.0 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + -5.5y + y2 = 0.0 + -0.3
-5.5y + y2 = 0.0 + -0.3

Combine like terms: 0.0 + -0.3 = -0.3
-5.5y + y2 = -0.3

The y term is -5.5y.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5y + 7.5625 + y2 = -0.3 + 7.5625

Reorder the terms:
7.5625 + -5.5y + y2 = -0.3 + 7.5625

Combine like terms: -0.3 + 7.5625 = 7.2625
7.5625 + -5.5y + y2 = 7.2625

Factor a perfect square on the left side:
(y + -2.75)(y + -2.75) = 7.2625

Calculate the square root of the right side: 2.694902596

Break this problem into two subproblems by setting 
(y + -2.75) equal to 2.694902596 and -2.694902596.

Subproblem 1
y + -2.75 = 2.694902596

Simplifying
y + -2.75 = 2.694902596

Reorder the terms:
-2.75 + y = 2.694902596

Solving
-2.75 + y = 2.694902596

Solving for variable 'y'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + y = 2.694902596 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + y = 2.694902596 + 2.75
y = 2.694902596 + 2.75

Combine like terms: 2.694902596 + 2.75 = 5.444902596
y = 5.444902596

Simplifying
y = 5.444902596

Subproblem 2
y + -2.75 = -2.694902596

Simplifying
y + -2.75 = -2.694902596

Reorder the terms:
-2.75 + y = -2.694902596

Solving
-2.75 + y = -2.694902596

Solving for variable 'y'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + y = -2.694902596 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + y = -2.694902596 + 2.75
y = -2.694902596 + 2.75

Combine like terms: -2.694902596 + 2.75 = 0.055097404
y = 0.055097404

Simplifying
y = 0.055097404

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.444902596, 0.055097404}