y^2+12y-3=0

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

Simplifying
y2 + 12y + -3 = 0

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

Solving
-3 + 12y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 12y + 3 + y2 = 0 + 3

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

Combine like terms: -3 + 3 = 0
0 + 12y + y2 = 0 + 3
12y + y2 = 0 + 3

Combine like terms: 0 + 3 = 3
12y + y2 = 3

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 = 3 + 36

Reorder the terms:
36 + 12y + y2 = 3 + 36

Combine like terms: 3 + 36 = 39
36 + 12y + y2 = 39

Factor a perfect square on the left side:
(y + 6)(y + 6) = 39

Calculate the square root of the right side: 6.244997998

Break this problem into two subproblems by setting 
(y + 6) equal to 6.244997998 and -6.244997998.

Subproblem 1
y + 6 = 6.244997998

Simplifying
y + 6 = 6.244997998

Reorder the terms:
6 + y = 6.244997998

Solving
6 + y = 6.244997998

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 = 6.244997998 + -6

Combine like terms: 6 + -6 = 0
0 + y = 6.244997998 + -6
y = 6.244997998 + -6

Combine like terms: 6.244997998 + -6 = 0.244997998
y = 0.244997998

Simplifying
y = 0.244997998

Subproblem 2
y + 6 = -6.244997998

Simplifying
y + 6 = -6.244997998

Reorder the terms:
6 + y = -6.244997998

Solving
6 + y = -6.244997998

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 = -6.244997998 + -6

Combine like terms: 6 + -6 = 0
0 + y = -6.244997998 + -6
y = -6.244997998 + -6

Combine like terms: -6.244997998 + -6 = -12.244997998
y = -12.244997998

Simplifying
y = -12.244997998

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.244997998, -12.244997998}