4y^2+20y+20=0

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Solution for 4y^2+20y+20=0 equation: 


Simplifying
4y2 + 20y + 20 = 0

Reorder the terms:
20 + 20y + 4y2 = 0

Solving
20 + 20y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + 5y + y2) = 0

Ignore the factor 4.

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

Simplifying
5 + 5y + y2 = 0

Solving
5 + 5y + y2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The y term is 5y.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5y + 6.25 + y2 = -5 + 6.25

Reorder the terms:
6.25 + 5y + y2 = -5 + 6.25

Combine like terms: -5 + 6.25 = 1.25
6.25 + 5y + y2 = 1.25

Factor a perfect square on the left side:
(y + 2.5)(y + 2.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(y + 2.5) equal to 1.118033989 and -1.118033989.


Subproblem 1
y + 2.5 = 1.118033989

Simplifying
y + 2.5 = 1.118033989

Reorder the terms:
2.5 + y = 1.118033989

Solving
2.5 + y = 1.118033989

Solving for variable 'y'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + y = 1.118033989 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = 1.118033989 + -2.5
y = 1.118033989 + -2.5

Combine like terms: 1.118033989 + -2.5 = -1.381966011
y = -1.381966011

Simplifying
y = -1.381966011


Subproblem 2
y + 2.5 = -1.118033989

Simplifying
y + 2.5 = -1.118033989

Reorder the terms:
2.5 + y = -1.118033989

Solving
2.5 + y = -1.118033989

Solving for variable 'y'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + y = -1.118033989 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = -1.118033989 + -2.5
y = -1.118033989 + -2.5

Combine like terms: -1.118033989 + -2.5 = -3.618033989
y = -3.618033989

Simplifying
y = -3.618033989


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-1.381966011, -3.618033989}
Solution
y = {-1.381966011, -3.618033989}

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