y^2+10=-12y

Solution for y^2+10=-12y equation:

Simplifying
y2 + 10 = -12y

Reorder the terms:
10 + y2 = -12y

Solving
10 + y2 = -12y

Solving for variable 'y'.

Reorder the terms:
10 + 12y + y2 = -12y + 12y

Combine like terms: -12y + 12y = 0
10 + 12y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 12y + -10 + y2 = 0 + -10

Reorder the terms:
10 + -10 + 12y + y2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 12y + y2 = 0 + -10
12y + y2 = 0 + -10

Combine like terms: 0 + -10 = -10
12y + y2 = -10

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 = -10 + 36

Reorder the terms:
36 + 12y + y2 = -10 + 36

Combine like terms: -10 + 36 = 26
36 + 12y + y2 = 26

Factor a perfect square on the left side:
(y + 6)(y + 6) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(y + 6) equal to 5.099019514 and -5.099019514.

Subproblem 1
y + 6 = 5.099019514

Simplifying
y + 6 = 5.099019514

Reorder the terms:
6 + y = 5.099019514

Solving
6 + y = 5.099019514

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 = 5.099019514 + -6

Combine like terms: 6 + -6 = 0
0 + y = 5.099019514 + -6
y = 5.099019514 + -6

Combine like terms: 5.099019514 + -6 = -0.900980486
y = -0.900980486

Simplifying
y = -0.900980486

Subproblem 2
y + 6 = -5.099019514

Simplifying
y + 6 = -5.099019514

Reorder the terms:
6 + y = -5.099019514

Solving
6 + y = -5.099019514

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 = -5.099019514 + -6

Combine like terms: 6 + -6 = 0
0 + y = -5.099019514 + -6
y = -5.099019514 + -6

Combine like terms: -5.099019514 + -6 = -11.099019514
y = -11.099019514

Simplifying
y = -11.099019514

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.900980486, -11.099019514}