8v(-4v+-32)=8

Solution for 8v(-4v+-32)=8 equation:

Simplifying
8v(-4v + -32) = 8

Reorder the terms:
8v(-32 + -4v) = 8
(-32 * 8v + -4v * 8v) = 8
(-256v + -32v2) = 8

Solving
-256v + -32v2 = 8

Solving for variable 'v'.

Reorder the terms:
-8 + -256v + -32v2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + -256v + -32v2 = 0

Factor out the Greatest Common Factor (GCF), '-8'.
-8(1 + 32v + 4v2) = 0

Ignore the factor -8.
Subproblem 1
Set the factor '(1 + 32v + 4v2)' equal to zero and attempt to solve:

Simplifying
1 + 32v + 4v2 = 0

Solving
1 + 32v + 4v2 = 0

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

Divide each side by '4'.
0.25 + 8v + v2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 8v + -0.25 + v2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 8v + v2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 8v + v2 = 0 + -0.25
8v + v2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
8v + v2 = -0.25

The v term is 8v.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8v + 16 + v2 = -0.25 + 16

Reorder the terms:
16 + 8v + v2 = -0.25 + 16

Combine like terms: -0.25 + 16 = 15.75
16 + 8v + v2 = 15.75

Factor a perfect square on the left side:
(v + 4)(v + 4) = 15.75

Calculate the square root of the right side: 3.968626967

Break this problem into two subproblems by setting 
(v + 4) equal to 3.968626967 and -3.968626967.

Subproblem 1
v + 4 = 3.968626967

Simplifying
v + 4 = 3.968626967

Reorder the terms:
4 + v = 3.968626967

Solving
4 + v = 3.968626967

Solving for variable 'v'.

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

Add '-4' to each side of the equation.
4 + -4 + v = 3.968626967 + -4

Combine like terms: 4 + -4 = 0
0 + v = 3.968626967 + -4
v = 3.968626967 + -4

Combine like terms: 3.968626967 + -4 = -0.031373033
v = -0.031373033

Simplifying
v = -0.031373033

Subproblem 2
v + 4 = -3.968626967

Simplifying
v + 4 = -3.968626967

Reorder the terms:
4 + v = -3.968626967

Solving
4 + v = -3.968626967

Solving for variable 'v'.

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

Add '-4' to each side of the equation.
4 + -4 + v = -3.968626967 + -4

Combine like terms: 4 + -4 = 0
0 + v = -3.968626967 + -4
v = -3.968626967 + -4

Combine like terms: -3.968626967 + -4 = -7.968626967
v = -7.968626967

Simplifying
v = -7.968626967

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-0.031373033, -7.968626967}
Solution
v = {-0.031373033, -7.968626967}