y^2+12y+20=4

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Solution for y^2+12y+20=4 equation: 


Simplifying
y2 + 12y + 20 = 4

Reorder the terms:
20 + 12y + y2 = 4

Solving
20 + 12y + y2 = 4

Solving for variable 'y'.

Reorder the terms:
20 + -4 + 12y + y2 = 4 + -4

Combine like terms: 20 + -4 = 16
16 + 12y + y2 = 4 + -4

Combine like terms: 4 + -4 = 0
16 + 12y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 12y + -16 + y2 = 0 + -16

Reorder the terms:
16 + -16 + 12y + y2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 12y + y2 = 0 + -16
12y + y2 = 0 + -16

Combine like terms: 0 + -16 = -16
12y + y2 = -16

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 = -16 + 36

Reorder the terms:
36 + 12y + y2 = -16 + 36

Combine like terms: -16 + 36 = 20
36 + 12y + y2 = 20

Factor a perfect square on the left side:
(y + 6)(y + 6) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(y + 6) equal to 4.472135955 and -4.472135955.


Subproblem 1
y + 6 = 4.472135955

Simplifying
y + 6 = 4.472135955

Reorder the terms:
6 + y = 4.472135955

Solving
6 + y = 4.472135955

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 = 4.472135955 + -6

Combine like terms: 6 + -6 = 0
0 + y = 4.472135955 + -6
y = 4.472135955 + -6

Combine like terms: 4.472135955 + -6 = -1.527864045
y = -1.527864045

Simplifying
y = -1.527864045


Subproblem 2
y + 6 = -4.472135955

Simplifying
y + 6 = -4.472135955

Reorder the terms:
6 + y = -4.472135955

Solving
6 + y = -4.472135955

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 = -4.472135955 + -6

Combine like terms: 6 + -6 = 0
0 + y = -4.472135955 + -6
y = -4.472135955 + -6

Combine like terms: -4.472135955 + -6 = -10.472135955
y = -10.472135955

Simplifying
y = -10.472135955


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-1.527864045, -10.472135955}

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