6v^2-12v-14=-8

Solution for 6v^2-12v-14=-8 equation:

Simplifying
6v2 + -12v + -14 = -8

Reorder the terms:
-14 + -12v + 6v2 = -8

Solving
-14 + -12v + 6v2 = -8

Solving for variable 'v'.

Reorder the terms:
-14 + 8 + -12v + 6v2 = -8 + 8

Combine like terms: -14 + 8 = -6
-6 + -12v + 6v2 = -8 + 8

Combine like terms: -8 + 8 = 0
-6 + -12v + 6v2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + -2v + v2) = 0

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

Simplifying
-1 + -2v + v2 = 0

Solving
-1 + -2v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -2v + 1 + v2 = 0 + 1

Reorder the terms:
-1 + 1 + -2v + v2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2v + v2 = 0 + 1
-2v + v2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2v + v2 = 1

The v term is -2v.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2v + 1 + v2 = 1 + 1

Reorder the terms:
1 + -2v + v2 = 1 + 1

Combine like terms: 1 + 1 = 2
1 + -2v + v2 = 2

Factor a perfect square on the left side:
(v + -1)(v + -1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(v + -1) equal to 1.414213562 and -1.414213562.

Subproblem 1
v + -1 = 1.414213562

Simplifying
v + -1 = 1.414213562

Reorder the terms:
-1 + v = 1.414213562

Solving
-1 + v = 1.414213562

Solving for variable 'v'.

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

Add '1' to each side of the equation.
-1 + 1 + v = 1.414213562 + 1

Combine like terms: -1 + 1 = 0
0 + v = 1.414213562 + 1
v = 1.414213562 + 1

Combine like terms: 1.414213562 + 1 = 2.414213562
v = 2.414213562

Simplifying
v = 2.414213562

Subproblem 2
v + -1 = -1.414213562

Simplifying
v + -1 = -1.414213562

Reorder the terms:
-1 + v = -1.414213562

Solving
-1 + v = -1.414213562

Solving for variable 'v'.

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

Add '1' to each side of the equation.
-1 + 1 + v = -1.414213562 + 1

Combine like terms: -1 + 1 = 0
0 + v = -1.414213562 + 1
v = -1.414213562 + 1

Combine like terms: -1.414213562 + 1 = -0.414213562
v = -0.414213562

Simplifying
v = -0.414213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {2.414213562, -0.414213562}
Solution
v = {2.414213562, -0.414213562}