3y^2+26y+12=0

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Solution for 3y^2+26y+12=0 equation: 


Simplifying
3y2 + 26y + 12 = 0

Reorder the terms:
12 + 26y + 3y2 = 0

Solving
12 + 26y + 3y2 = 0

Solving for variable 'y'.

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

Divide each side by '3'.
4 + 8.666666667y + y2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 8.666666667y + -4 + y2 = 0 + -4

Reorder the terms:
4 + -4 + 8.666666667y + y2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 8.666666667y + y2 = 0 + -4
8.666666667y + y2 = 0 + -4

Combine like terms: 0 + -4 = -4
8.666666667y + y2 = -4

The y term is 8.666666667y.  Take half its coefficient (4.333333334).
Square it (18.77777778) and add it to both sides.

Add '18.77777778' to each side of the equation.
8.666666667y + 18.77777778 + y2 = -4 + 18.77777778

Reorder the terms:
18.77777778 + 8.666666667y + y2 = -4 + 18.77777778

Combine like terms: -4 + 18.77777778 = 14.77777778
18.77777778 + 8.666666667y + y2 = 14.77777778

Factor a perfect square on the left side:
(y + 4.333333334)(y + 4.333333334) = 14.77777778

Calculate the square root of the right side: 3.844187532

Break this problem into two subproblems by setting 
(y + 4.333333334) equal to 3.844187532 and -3.844187532.


Subproblem 1
y + 4.333333334 = 3.844187532

Simplifying
y + 4.333333334 = 3.844187532

Reorder the terms:
4.333333334 + y = 3.844187532

Solving
4.333333334 + y = 3.844187532

Solving for variable 'y'.

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

Add '-4.333333334' to each side of the equation.
4.333333334 + -4.333333334 + y = 3.844187532 + -4.333333334

Combine like terms: 4.333333334 + -4.333333334 = 0.000000000
0.000000000 + y = 3.844187532 + -4.333333334
y = 3.844187532 + -4.333333334

Combine like terms: 3.844187532 + -4.333333334 = -0.489145802
y = -0.489145802

Simplifying
y = -0.489145802


Subproblem 2
y + 4.333333334 = -3.844187532

Simplifying
y + 4.333333334 = -3.844187532

Reorder the terms:
4.333333334 + y = -3.844187532

Solving
4.333333334 + y = -3.844187532

Solving for variable 'y'.

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

Add '-4.333333334' to each side of the equation.
4.333333334 + -4.333333334 + y = -3.844187532 + -4.333333334

Combine like terms: 4.333333334 + -4.333333334 = 0.000000000
0.000000000 + y = -3.844187532 + -4.333333334
y = -3.844187532 + -4.333333334

Combine like terms: -3.844187532 + -4.333333334 = -8.177520866
y = -8.177520866

Simplifying
y = -8.177520866


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.489145802, -8.177520866}

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