y^2+12y-5=0

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

Simplifying
y2 + 12y + -5 = 0

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

Solving
-5 + 12y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 12y + 5 + y2 = 0 + 5

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

Combine like terms: -5 + 5 = 0
0 + 12y + y2 = 0 + 5
12y + y2 = 0 + 5

Combine like terms: 0 + 5 = 5
12y + y2 = 5

The y term is 12y.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12y + 36 + y2 = 5 + 36

Reorder the terms:
36 + 12y + y2 = 5 + 36

Combine like terms: 5 + 36 = 41
36 + 12y + y2 = 41

Factor a perfect square on the left side:
(y + 6)(y + 6) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(y + 6) equal to 6.403124237 and -6.403124237.

Subproblem 1
y + 6 = 6.403124237

Simplifying
y + 6 = 6.403124237

Reorder the terms:
6 + y = 6.403124237

Solving
6 + y = 6.403124237

Solving for variable 'y'.

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

Add '-6' to each side of the equation.
6 + -6 + y = 6.403124237 + -6

Combine like terms: 6 + -6 = 0
0 + y = 6.403124237 + -6
y = 6.403124237 + -6

Combine like terms: 6.403124237 + -6 = 0.403124237
y = 0.403124237

Simplifying
y = 0.403124237

Subproblem 2
y + 6 = -6.403124237

Simplifying
y + 6 = -6.403124237

Reorder the terms:
6 + y = -6.403124237

Solving
6 + y = -6.403124237

Solving for variable 'y'.

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

Add '-6' to each side of the equation.
6 + -6 + y = -6.403124237 + -6

Combine like terms: 6 + -6 = 0
0 + y = -6.403124237 + -6
y = -6.403124237 + -6

Combine like terms: -6.403124237 + -6 = -12.403124237
y = -12.403124237

Simplifying
y = -12.403124237

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.403124237, -12.403124237}