2(2v-6)+2=6-8(2v-3)v

Solution for 2(2v-6)+2=6-8(2v-3)v equation:

Simplifying
2(2v + -6) + 2 = 6 + -8(2v + -3) * v

Reorder the terms:
2(-6 + 2v) + 2 = 6 + -8(2v + -3) * v
(-6 * 2 + 2v * 2) + 2 = 6 + -8(2v + -3) * v
(-12 + 4v) + 2 = 6 + -8(2v + -3) * v

Reorder the terms:
-12 + 2 + 4v = 6 + -8(2v + -3) * v

Combine like terms: -12 + 2 = -10
-10 + 4v = 6 + -8(2v + -3) * v

Reorder the terms:
-10 + 4v = 6 + -8(-3 + 2v) * v

Reorder the terms for easier multiplication:
-10 + 4v = 6 + -8v(-3 + 2v)
-10 + 4v = 6 + (-3 * -8v + 2v * -8v)
-10 + 4v = 6 + (24v + -16v2)

Solving
-10 + 4v = 6 + 24v + -16v2

Solving for variable 'v'.

Reorder the terms:
-10 + -6 + 4v + -24v + 16v2 = 6 + 24v + -16v2 + -6 + -24v + 16v2

Combine like terms: -10 + -6 = -16
-16 + 4v + -24v + 16v2 = 6 + 24v + -16v2 + -6 + -24v + 16v2

Combine like terms: 4v + -24v = -20v
-16 + -20v + 16v2 = 6 + 24v + -16v2 + -6 + -24v + 16v2

Reorder the terms:
-16 + -20v + 16v2 = 6 + -6 + 24v + -24v + -16v2 + 16v2

Combine like terms: 6 + -6 = 0
-16 + -20v + 16v2 = 0 + 24v + -24v + -16v2 + 16v2
-16 + -20v + 16v2 = 24v + -24v + -16v2 + 16v2

Combine like terms: 24v + -24v = 0
-16 + -20v + 16v2 = 0 + -16v2 + 16v2
-16 + -20v + 16v2 = -16v2 + 16v2

Combine like terms: -16v2 + 16v2 = 0
-16 + -20v + 16v2 = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor '(-4 + -5v + 4v2)' equal to zero and attempt to solve:

Simplifying
-4 + -5v + 4v2 = 0

Solving
-4 + -5v + 4v2 = 0

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

Divide each side by '4'.
-1 + -1.25v + v2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1.25v + 1 + v2 = 0 + 1

Reorder the terms:
-1 + 1 + -1.25v + v2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1.25v + v2 = 0 + 1
-1.25v + v2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1.25v + v2 = 1

The v term is -1.25v.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25v + 0.390625 + v2 = 1 + 0.390625

Reorder the terms:
0.390625 + -1.25v + v2 = 1 + 0.390625

Combine like terms: 1 + 0.390625 = 1.390625
0.390625 + -1.25v + v2 = 1.390625

Factor a perfect square on the left side:
(v + -0.625)(v + -0.625) = 1.390625

Calculate the square root of the right side: 1.179247642

Break this problem into two subproblems by setting 
(v + -0.625) equal to 1.179247642 and -1.179247642.

Subproblem 1
v + -0.625 = 1.179247642

Simplifying
v + -0.625 = 1.179247642

Reorder the terms:
-0.625 + v = 1.179247642

Solving
-0.625 + v = 1.179247642

Solving for variable 'v'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + v = 1.179247642 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + v = 1.179247642 + 0.625
v = 1.179247642 + 0.625

Combine like terms: 1.179247642 + 0.625 = 1.804247642
v = 1.804247642

Simplifying
v = 1.804247642

Subproblem 2
v + -0.625 = -1.179247642

Simplifying
v + -0.625 = -1.179247642

Reorder the terms:
-0.625 + v = -1.179247642

Solving
-0.625 + v = -1.179247642

Solving for variable 'v'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + v = -1.179247642 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + v = -1.179247642 + 0.625
v = -1.179247642 + 0.625

Combine like terms: -1.179247642 + 0.625 = -0.554247642
v = -0.554247642

Simplifying
v = -0.554247642

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {1.804247642, -0.554247642}
Solution
v = {1.804247642, -0.554247642}