y(3y+11)=11

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Solution for y(3y+11)=11 equation: 


Simplifying
y(3y + 11) = 11

Reorder the terms:
y(11 + 3y) = 11
(11 * y + 3y * y) = 11
(11y + 3y2) = 11

Solving
11y + 3y2 = 11

Solving for variable 'y'.

Reorder the terms:
-11 + 11y + 3y2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + 11y + 3y2 = 0

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

Divide each side by '3'.
-3.666666667 + 3.666666667y + y2 = 0

Move the constant term to the right:

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667y + 3.666666667 + y2 = 0 + 3.666666667

Reorder the terms:
-3.666666667 + 3.666666667 + 3.666666667y + y2 = 0 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + 3.666666667y + y2 = 0 + 3.666666667
3.666666667y + y2 = 0 + 3.666666667

Combine like terms: 0 + 3.666666667 = 3.666666667
3.666666667y + y2 = 3.666666667

The y term is 3.666666667y.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667y + 3.361111114 + y2 = 3.666666667 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667y + y2 = 3.666666667 + 3.361111114

Combine like terms: 3.666666667 + 3.361111114 = 7.027777781
3.361111114 + 3.666666667y + y2 = 7.027777781

Factor a perfect square on the left side:
(y + 1.833333334)(y + 1.833333334) = 7.027777781

Calculate the square root of the right side: 2.650995621

Break this problem into two subproblems by setting 
(y + 1.833333334) equal to 2.650995621 and -2.650995621.


Subproblem 1
y + 1.833333334 = 2.650995621

Simplifying
y + 1.833333334 = 2.650995621

Reorder the terms:
1.833333334 + y = 2.650995621

Solving
1.833333334 + y = 2.650995621

Solving for variable 'y'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + y = 2.650995621 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + y = 2.650995621 + -1.833333334
y = 2.650995621 + -1.833333334

Combine like terms: 2.650995621 + -1.833333334 = 0.817662287
y = 0.817662287

Simplifying
y = 0.817662287


Subproblem 2
y + 1.833333334 = -2.650995621

Simplifying
y + 1.833333334 = -2.650995621

Reorder the terms:
1.833333334 + y = -2.650995621

Solving
1.833333334 + y = -2.650995621

Solving for variable 'y'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + y = -2.650995621 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + y = -2.650995621 + -1.833333334
y = -2.650995621 + -1.833333334

Combine like terms: -2.650995621 + -1.833333334 = -4.484328955
y = -4.484328955

Simplifying
y = -4.484328955


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.817662287, -4.484328955}

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