4y^2+28y+12=0

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Solution for 4y^2+28y+12=0 equation: 


Simplifying
4y2 + 28y + 12 = 0

Reorder the terms:
12 + 28y + 4y2 = 0

Solving
12 + 28y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 7y + y2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(3 + 7y + y2)' equal to zero and attempt to solve:

Simplifying
3 + 7y + y2 = 0

Solving
3 + 7y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 7y + -3 + y2 = 0 + -3

Reorder the terms:
3 + -3 + 7y + y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7y + y2 = 0 + -3
7y + y2 = 0 + -3

Combine like terms: 0 + -3 = -3
7y + y2 = -3

The y term is 7y.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7y + 12.25 + y2 = -3 + 12.25

Reorder the terms:
12.25 + 7y + y2 = -3 + 12.25

Combine like terms: -3 + 12.25 = 9.25
12.25 + 7y + y2 = 9.25

Factor a perfect square on the left side:
(y + 3.5)(y + 3.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(y + 3.5) equal to 3.041381265 and -3.041381265.


Subproblem 1
y + 3.5 = 3.041381265

Simplifying
y + 3.5 = 3.041381265

Reorder the terms:
3.5 + y = 3.041381265

Solving
3.5 + y = 3.041381265

Solving for variable 'y'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + y = 3.041381265 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + y = 3.041381265 + -3.5
y = 3.041381265 + -3.5

Combine like terms: 3.041381265 + -3.5 = -0.458618735
y = -0.458618735

Simplifying
y = -0.458618735


Subproblem 2
y + 3.5 = -3.041381265

Simplifying
y + 3.5 = -3.041381265

Reorder the terms:
3.5 + y = -3.041381265

Solving
3.5 + y = -3.041381265

Solving for variable 'y'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + y = -3.041381265 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + y = -3.041381265 + -3.5
y = -3.041381265 + -3.5

Combine like terms: -3.041381265 + -3.5 = -6.541381265
y = -6.541381265

Simplifying
y = -6.541381265


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.458618735, -6.541381265}
Solution
y = {-0.458618735, -6.541381265}

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