4v^2+20v+12=0

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Solution for 4v^2+20v+12=0 equation: 


Simplifying
4v2 + 20v + 12 = 0

Reorder the terms:
12 + 20v + 4v2 = 0

Solving
12 + 20v + 4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 5v + v2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(3 + 5v + v2)' equal to zero and attempt to solve:

Simplifying
3 + 5v + v2 = 0

Solving
3 + 5v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 5v + -3 + v2 = 0 + -3

Reorder the terms:
3 + -3 + 5v + v2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5v + v2 = 0 + -3
5v + v2 = 0 + -3

Combine like terms: 0 + -3 = -3
5v + v2 = -3

The v term is 5v.  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.
5v + 6.25 + v2 = -3 + 6.25

Reorder the terms:
6.25 + 5v + v2 = -3 + 6.25

Combine like terms: -3 + 6.25 = 3.25
6.25 + 5v + v2 = 3.25

Factor a perfect square on the left side:
(v + 2.5)(v + 2.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(v + 2.5) equal to 1.802775638 and -1.802775638.


Subproblem 1
v + 2.5 = 1.802775638

Simplifying
v + 2.5 = 1.802775638

Reorder the terms:
2.5 + v = 1.802775638

Solving
2.5 + v = 1.802775638

Solving for variable 'v'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + v = 1.802775638 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + v = 1.802775638 + -2.5
v = 1.802775638 + -2.5

Combine like terms: 1.802775638 + -2.5 = -0.697224362
v = -0.697224362

Simplifying
v = -0.697224362


Subproblem 2
v + 2.5 = -1.802775638

Simplifying
v + 2.5 = -1.802775638

Reorder the terms:
2.5 + v = -1.802775638

Solving
2.5 + v = -1.802775638

Solving for variable 'v'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + v = -1.802775638 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + v = -1.802775638 + -2.5
v = -1.802775638 + -2.5

Combine like terms: -1.802775638 + -2.5 = -4.302775638
v = -4.302775638

Simplifying
v = -4.302775638


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-0.697224362, -4.302775638}
Solution
v = {-0.697224362, -4.302775638}

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