12v^2+6v-8=-4

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Solution for 12v^2+6v-8=-4 equation: 


Simplifying
12v2 + 6v + -8 = -4

Reorder the terms:
-8 + 6v + 12v2 = -4

Solving
-8 + 6v + 12v2 = -4

Solving for variable 'v'.

Reorder the terms:
-8 + 4 + 6v + 12v2 = -4 + 4

Combine like terms: -8 + 4 = -4
-4 + 6v + 12v2 = -4 + 4

Combine like terms: -4 + 4 = 0
-4 + 6v + 12v2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 3v + 6v2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + 3v + 6v2)' equal to zero and attempt to solve:

Simplifying
-2 + 3v + 6v2 = 0

Solving
-2 + 3v + 6v2 = 0

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
-0.3333333333 + 0.5v + v2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 0.5v + 0.3333333333 + v2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 0.5v + v2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 0.5v + v2 = 0 + 0.3333333333
0.5v + v2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
0.5v + v2 = 0.3333333333

The v term is 0.5v.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5v + 0.0625 + v2 = 0.3333333333 + 0.0625

Reorder the terms:
0.0625 + 0.5v + v2 = 0.3333333333 + 0.0625

Combine like terms: 0.3333333333 + 0.0625 = 0.3958333333
0.0625 + 0.5v + v2 = 0.3958333333

Factor a perfect square on the left side:
(v + 0.25)(v + 0.25) = 0.3958333333

Calculate the square root of the right side: 0.62915287

Break this problem into two subproblems by setting 
(v + 0.25) equal to 0.62915287 and -0.62915287.


Subproblem 1
v + 0.25 = 0.62915287

Simplifying
v + 0.25 = 0.62915287

Reorder the terms:
0.25 + v = 0.62915287

Solving
0.25 + v = 0.62915287

Solving for variable 'v'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + v = 0.62915287 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + v = 0.62915287 + -0.25
v = 0.62915287 + -0.25

Combine like terms: 0.62915287 + -0.25 = 0.37915287
v = 0.37915287

Simplifying
v = 0.37915287


Subproblem 2
v + 0.25 = -0.62915287

Simplifying
v + 0.25 = -0.62915287

Reorder the terms:
0.25 + v = -0.62915287

Solving
0.25 + v = -0.62915287

Solving for variable 'v'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + v = -0.62915287 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + v = -0.62915287 + -0.25
v = -0.62915287 + -0.25

Combine like terms: -0.62915287 + -0.25 = -0.87915287
v = -0.87915287

Simplifying
v = -0.87915287


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {0.37915287, -0.87915287}
Solution
v = {0.37915287, -0.87915287}

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