3*y^2-12y=11

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Solution for 3*y^2-12y=11 equation:


Simplifying
3y2 + -12y = 11

Reorder the terms:
-12y + 3y2 = 11

Solving
-12y + 3y2 = 11

Solving for variable 'y'.

Reorder the terms:
-11 + -12y + 3y2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + -12y + 3y2 = 0

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

Divide each side by '3'.
-3.666666667 + -4y + y2 = 0

Move the constant term to the right:

Add '3.666666667' to each side of the equation.
-3.666666667 + -4y + 3.666666667 + y2 = 0 + 3.666666667

Reorder the terms:
-3.666666667 + 3.666666667 + -4y + y2 = 0 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + -4y + y2 = 0 + 3.666666667
-4y + y2 = 0 + 3.666666667

Combine like terms: 0 + 3.666666667 = 3.666666667
-4y + y2 = 3.666666667

The y term is -4y.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4y + 4 + y2 = 3.666666667 + 4

Reorder the terms:
4 + -4y + y2 = 3.666666667 + 4

Combine like terms: 3.666666667 + 4 = 7.666666667
4 + -4y + y2 = 7.666666667

Factor a perfect square on the left side:
(y + -2)(y + -2) = 7.666666667

Calculate the square root of the right side: 2.768874621

Break this problem into two subproblems by setting 
(y + -2) equal to 2.768874621 and -2.768874621.


Subproblem 1
y + -2 = 2.768874621

Simplifying
y + -2 = 2.768874621

Reorder the terms:
-2 + y = 2.768874621

Solving
-2 + y = 2.768874621

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = 2.768874621 + 2

Combine like terms: -2 + 2 = 0
0 + y = 2.768874621 + 2
y = 2.768874621 + 2

Combine like terms: 2.768874621 + 2 = 4.768874621
y = 4.768874621

Simplifying
y = 4.768874621


Subproblem 2
y + -2 = -2.768874621

Simplifying
y + -2 = -2.768874621

Reorder the terms:
-2 + y = -2.768874621

Solving
-2 + y = -2.768874621

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = -2.768874621 + 2

Combine like terms: -2 + 2 = 0
0 + y = -2.768874621 + 2
y = -2.768874621 + 2

Combine like terms: -2.768874621 + 2 = -0.768874621
y = -0.768874621

Simplifying
y = -0.768874621


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.768874621, -0.768874621}

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