4v^2+104v-12=0

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Solution for 4v^2+104v-12=0 equation: 


Simplifying
4v2 + 104v + -12 = 0

Reorder the terms:
-12 + 104v + 4v2 = 0

Solving
-12 + 104v + 4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + 26v + v2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-3 + 26v + v2)' equal to zero and attempt to solve:

Simplifying
-3 + 26v + v2 = 0

Solving
-3 + 26v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 26v + 3 + v2 = 0 + 3

Reorder the terms:
-3 + 3 + 26v + v2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 26v + v2 = 0 + 3
26v + v2 = 0 + 3

Combine like terms: 0 + 3 = 3
26v + v2 = 3

The v term is 26v.  Take half its coefficient (13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
26v + 169 + v2 = 3 + 169

Reorder the terms:
169 + 26v + v2 = 3 + 169

Combine like terms: 3 + 169 = 172
169 + 26v + v2 = 172

Factor a perfect square on the left side:
(v + 13)(v + 13) = 172

Calculate the square root of the right side: 13.114877049

Break this problem into two subproblems by setting 
(v + 13) equal to 13.114877049 and -13.114877049.


Subproblem 1
v + 13 = 13.114877049

Simplifying
v + 13 = 13.114877049

Reorder the terms:
13 + v = 13.114877049

Solving
13 + v = 13.114877049

Solving for variable 'v'.

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

Add '-13' to each side of the equation.
13 + -13 + v = 13.114877049 + -13

Combine like terms: 13 + -13 = 0
0 + v = 13.114877049 + -13
v = 13.114877049 + -13

Combine like terms: 13.114877049 + -13 = 0.114877049
v = 0.114877049

Simplifying
v = 0.114877049


Subproblem 2
v + 13 = -13.114877049

Simplifying
v + 13 = -13.114877049

Reorder the terms:
13 + v = -13.114877049

Solving
13 + v = -13.114877049

Solving for variable 'v'.

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

Add '-13' to each side of the equation.
13 + -13 + v = -13.114877049 + -13

Combine like terms: 13 + -13 = 0
0 + v = -13.114877049 + -13
v = -13.114877049 + -13

Combine like terms: -13.114877049 + -13 = -26.114877049
v = -26.114877049

Simplifying
v = -26.114877049


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {0.114877049, -26.114877049}
Solution
v = {0.114877049, -26.114877049}

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