3y^2+16y+12=0

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Solution for 3y^2+16y+12=0 equation: 


Simplifying
3y2 + 16y + 12 = 0

Reorder the terms:
12 + 16y + 3y2 = 0

Solving
12 + 16y + 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 + 5.333333333y + y2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 5.333333333y + -4 + y2 = 0 + -4

Reorder the terms:
4 + -4 + 5.333333333y + y2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5.333333333y + y2 = 0 + -4
5.333333333y + y2 = 0 + -4

Combine like terms: 0 + -4 = -4
5.333333333y + y2 = -4

The y term is 5.333333333y.  Take half its coefficient (2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
5.333333333y + 7.111111113 + y2 = -4 + 7.111111113

Reorder the terms:
7.111111113 + 5.333333333y + y2 = -4 + 7.111111113

Combine like terms: -4 + 7.111111113 = 3.111111113
7.111111113 + 5.333333333y + y2 = 3.111111113

Factor a perfect square on the left side:
(y + 2.666666667)(y + 2.666666667) = 3.111111113

Calculate the square root of the right side: 1.763834208

Break this problem into two subproblems by setting 
(y + 2.666666667) equal to 1.763834208 and -1.763834208.


Subproblem 1
y + 2.666666667 = 1.763834208

Simplifying
y + 2.666666667 = 1.763834208

Reorder the terms:
2.666666667 + y = 1.763834208

Solving
2.666666667 + y = 1.763834208

Solving for variable 'y'.

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

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.666666667 + y = 1.763834208 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + y = 1.763834208 + -2.666666667
y = 1.763834208 + -2.666666667

Combine like terms: 1.763834208 + -2.666666667 = -0.902832459
y = -0.902832459

Simplifying
y = -0.902832459


Subproblem 2
y + 2.666666667 = -1.763834208

Simplifying
y + 2.666666667 = -1.763834208

Reorder the terms:
2.666666667 + y = -1.763834208

Solving
2.666666667 + y = -1.763834208

Solving for variable 'y'.

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

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.666666667 + y = -1.763834208 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + y = -1.763834208 + -2.666666667
y = -1.763834208 + -2.666666667

Combine like terms: -1.763834208 + -2.666666667 = -4.430500875
y = -4.430500875

Simplifying
y = -4.430500875


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.902832459, -4.430500875}

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