3y^2+24y+12=0

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Solution for 3y^2+24y+12=0 equation: 


Simplifying
3y2 + 24y + 12 = 0

Reorder the terms:
12 + 24y + 3y2 = 0

Solving
12 + 24y + 3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + 8y + y2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(4 + 8y + y2)' equal to zero and attempt to solve:

Simplifying
4 + 8y + y2 = 0

Solving
4 + 8y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 8y + -4 + y2 = 0 + -4

Reorder the terms:
4 + -4 + 8y + y2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 8y + y2 = 0 + -4
8y + y2 = 0 + -4

Combine like terms: 0 + -4 = -4
8y + y2 = -4

The y term is 8y.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8y + 16 + y2 = -4 + 16

Reorder the terms:
16 + 8y + y2 = -4 + 16

Combine like terms: -4 + 16 = 12
16 + 8y + y2 = 12

Factor a perfect square on the left side:
(y + 4)(y + 4) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(y + 4) equal to 3.464101615 and -3.464101615.


Subproblem 1
y + 4 = 3.464101615

Simplifying
y + 4 = 3.464101615

Reorder the terms:
4 + y = 3.464101615

Solving
4 + y = 3.464101615

Solving for variable 'y'.

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

Add '-4' to each side of the equation.
4 + -4 + y = 3.464101615 + -4

Combine like terms: 4 + -4 = 0
0 + y = 3.464101615 + -4
y = 3.464101615 + -4

Combine like terms: 3.464101615 + -4 = -0.535898385
y = -0.535898385

Simplifying
y = -0.535898385


Subproblem 2
y + 4 = -3.464101615

Simplifying
y + 4 = -3.464101615

Reorder the terms:
4 + y = -3.464101615

Solving
4 + y = -3.464101615

Solving for variable 'y'.

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

Add '-4' to each side of the equation.
4 + -4 + y = -3.464101615 + -4

Combine like terms: 4 + -4 = 0
0 + y = -3.464101615 + -4
y = -3.464101615 + -4

Combine like terms: -3.464101615 + -4 = -7.464101615
y = -7.464101615

Simplifying
y = -7.464101615


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.535898385, -7.464101615}
Solution
y = {-0.535898385, -7.464101615}

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