4v^2+12v+4=0

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Solution for 4v^2+12v+4=0 equation: 


Simplifying
4v2 + 12v + 4 = 0

Reorder the terms:
4 + 12v + 4v2 = 0

Solving
4 + 12v + 4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 3v + v2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(1 + 3v + v2)' equal to zero and attempt to solve:

Simplifying
1 + 3v + v2 = 0

Solving
1 + 3v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 3v + -1 + v2 = 0 + -1

Reorder the terms:
1 + -1 + 3v + v2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3v + v2 = 0 + -1
3v + v2 = 0 + -1

Combine like terms: 0 + -1 = -1
3v + v2 = -1

The v term is 3v.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3v + 2.25 + v2 = -1 + 2.25

Reorder the terms:
2.25 + 3v + v2 = -1 + 2.25

Combine like terms: -1 + 2.25 = 1.25
2.25 + 3v + v2 = 1.25

Factor a perfect square on the left side:
(v + 1.5)(v + 1.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(v + 1.5) equal to 1.118033989 and -1.118033989.


Subproblem 1
v + 1.5 = 1.118033989

Simplifying
v + 1.5 = 1.118033989

Reorder the terms:
1.5 + v = 1.118033989

Solving
1.5 + v = 1.118033989

Solving for variable 'v'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + v = 1.118033989 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + v = 1.118033989 + -1.5
v = 1.118033989 + -1.5

Combine like terms: 1.118033989 + -1.5 = -0.381966011
v = -0.381966011

Simplifying
v = -0.381966011


Subproblem 2
v + 1.5 = -1.118033989

Simplifying
v + 1.5 = -1.118033989

Reorder the terms:
1.5 + v = -1.118033989

Solving
1.5 + v = -1.118033989

Solving for variable 'v'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + v = -1.118033989 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + v = -1.118033989 + -1.5
v = -1.118033989 + -1.5

Combine like terms: -1.118033989 + -1.5 = -2.618033989
v = -2.618033989

Simplifying
v = -2.618033989


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-0.381966011, -2.618033989}
Solution
v = {-0.381966011, -2.618033989}

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