4-2v(v-6)=-8

Solution for 4-2v(v-6)=-8 equation:

Simplifying
4 + -2v(v + -6) = -8

Reorder the terms:
4 + -2v(-6 + v) = -8
4 + (-6 * -2v + v * -2v) = -8
4 + (12v + -2v2) = -8

Solving
4 + 12v + -2v2 = -8

Solving for variable 'v'.

Reorder the terms:
4 + 8 + 12v + -2v2 = -8 + 8

Combine like terms: 4 + 8 = 12
12 + 12v + -2v2 = -8 + 8

Combine like terms: -8 + 8 = 0
12 + 12v + -2v2 = 0

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

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

Simplifying
6 + 6v + -1v2 = 0

Solving
6 + 6v + -1v2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-6 + -6v + v2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -6v + 6 + v2 = 0 + 6

Reorder the terms:
-6 + 6 + -6v + v2 = 0 + 6

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

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

The v term is -6v.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6v + 9 + v2 = 6 + 9

Reorder the terms:
9 + -6v + v2 = 6 + 9

Combine like terms: 6 + 9 = 15
9 + -6v + v2 = 15

Factor a perfect square on the left side:
(v + -3)(v + -3) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(v + -3) equal to 3.872983346 and -3.872983346.

Subproblem 1
v + -3 = 3.872983346

Simplifying
v + -3 = 3.872983346

Reorder the terms:
-3 + v = 3.872983346

Solving
-3 + v = 3.872983346

Solving for variable 'v'.

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

Add '3' to each side of the equation.
-3 + 3 + v = 3.872983346 + 3

Combine like terms: -3 + 3 = 0
0 + v = 3.872983346 + 3
v = 3.872983346 + 3

Combine like terms: 3.872983346 + 3 = 6.872983346
v = 6.872983346

Simplifying
v = 6.872983346

Subproblem 2
v + -3 = -3.872983346

Simplifying
v + -3 = -3.872983346

Reorder the terms:
-3 + v = -3.872983346

Solving
-3 + v = -3.872983346

Solving for variable 'v'.

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

Add '3' to each side of the equation.
-3 + 3 + v = -3.872983346 + 3

Combine like terms: -3 + 3 = 0
0 + v = -3.872983346 + 3
v = -3.872983346 + 3

Combine like terms: -3.872983346 + 3 = -0.872983346
v = -0.872983346

Simplifying
v = -0.872983346

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {6.872983346, -0.872983346}
Solution
v = {6.872983346, -0.872983346}