-3y^2-12y-5=0

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Solution for -3y^2-12y-5=0 equation: 


Simplifying
-3y2 + -12y + -5 = 0

Reorder the terms:
-5 + -12y + -3y2 = 0

Solving
-5 + -12y + -3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 12y + 3y2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + 12y + 3y2)' equal to zero and attempt to solve:

Simplifying
5 + 12y + 3y2 = 0

Solving
5 + 12y + 3y2 = 0

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

Divide each side by '3'.
1.666666667 + 4y + y2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + 4y + -1.666666667 + y2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + 4y + y2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + 4y + y2 = 0 + -1.666666667
4y + y2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
4y + y2 = -1.666666667

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 = -1.666666667 + 4

Reorder the terms:
4 + 4y + y2 = -1.666666667 + 4

Combine like terms: -1.666666667 + 4 = 2.333333333
4 + 4y + y2 = 2.333333333

Factor a perfect square on the left side:
(y + 2)(y + 2) = 2.333333333

Calculate the square root of the right side: 1.527525232

Break this problem into two subproblems by setting 
(y + 2) equal to 1.527525232 and -1.527525232.


Subproblem 1
y + 2 = 1.527525232

Simplifying
y + 2 = 1.527525232

Reorder the terms:
2 + y = 1.527525232

Solving
2 + y = 1.527525232

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 = 1.527525232 + -2

Combine like terms: 2 + -2 = 0
0 + y = 1.527525232 + -2
y = 1.527525232 + -2

Combine like terms: 1.527525232 + -2 = -0.472474768
y = -0.472474768

Simplifying
y = -0.472474768


Subproblem 2
y + 2 = -1.527525232

Simplifying
y + 2 = -1.527525232

Reorder the terms:
2 + y = -1.527525232

Solving
2 + y = -1.527525232

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 = -1.527525232 + -2

Combine like terms: 2 + -2 = 0
0 + y = -1.527525232 + -2
y = -1.527525232 + -2

Combine like terms: -1.527525232 + -2 = -3.527525232
y = -3.527525232

Simplifying
y = -3.527525232


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.472474768, -3.527525232}
Solution
y = {-0.472474768, -3.527525232}

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