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

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

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

Reorder the terms:
2(8 + v) = -4(4v + -8) * 8v
(8 * 2 + v * 2) = -4(4v + -8) * 8v
(16 + 2v) = -4(4v + -8) * 8v

Reorder the terms:
16 + 2v = -4(-8 + 4v) * 8v

Reorder the terms for easier multiplication:
16 + 2v = -4 * 8v(-8 + 4v)

Multiply -4 * 8
16 + 2v = -32v(-8 + 4v)
16 + 2v = (-8 * -32v + 4v * -32v)
16 + 2v = (256v + -128v2)

Solving
16 + 2v = 256v + -128v2

Solving for variable 'v'.

Combine like terms: 2v + -256v = -254v
16 + -254v + 128v2 = 256v + -128v2 + -256v + 128v2

Reorder the terms:
16 + -254v + 128v2 = 256v + -256v + -128v2 + 128v2

Combine like terms: 256v + -256v = 0
16 + -254v + 128v2 = 0 + -128v2 + 128v2
16 + -254v + 128v2 = -128v2 + 128v2

Combine like terms: -128v2 + 128v2 = 0
16 + -254v + 128v2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -127v + 64v2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + -127v + 64v2)' equal to zero and attempt to solve:

Simplifying
8 + -127v + 64v2 = 0

Solving
8 + -127v + 64v2 = 0

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

Divide each side by '64'.
0.125 + -1.984375v + v2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + -1.984375v + -0.125 + v2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + -1.984375v + v2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + -1.984375v + v2 = 0 + -0.125
-1.984375v + v2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
-1.984375v + v2 = -0.125

The v term is -1.984375v.  Take half its coefficient (-0.9921875).
Square it (0.9844360352) and add it to both sides.

Add '0.9844360352' to each side of the equation.
-1.984375v + 0.9844360352 + v2 = -0.125 + 0.9844360352

Reorder the terms:
0.9844360352 + -1.984375v + v2 = -0.125 + 0.9844360352

Combine like terms: -0.125 + 0.9844360352 = 0.8594360352
0.9844360352 + -1.984375v + v2 = 0.8594360352

Factor a perfect square on the left side:
(v + -0.9921875)(v + -0.9921875) = 0.8594360352

Calculate the square root of the right side: 0.92705773

Break this problem into two subproblems by setting 
(v + -0.9921875) equal to 0.92705773 and -0.92705773.

Subproblem 1
v + -0.9921875 = 0.92705773

Simplifying
v + -0.9921875 = 0.92705773

Reorder the terms:
-0.9921875 + v = 0.92705773

Solving
-0.9921875 + v = 0.92705773

Solving for variable 'v'.

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

Add '0.9921875' to each side of the equation.
-0.9921875 + 0.9921875 + v = 0.92705773 + 0.9921875

Combine like terms: -0.9921875 + 0.9921875 = 0.0000000
0.0000000 + v = 0.92705773 + 0.9921875
v = 0.92705773 + 0.9921875

Combine like terms: 0.92705773 + 0.9921875 = 1.91924523
v = 1.91924523

Simplifying
v = 1.91924523

Subproblem 2
v + -0.9921875 = -0.92705773

Simplifying
v + -0.9921875 = -0.92705773

Reorder the terms:
-0.9921875 + v = -0.92705773

Solving
-0.9921875 + v = -0.92705773

Solving for variable 'v'.

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

Add '0.9921875' to each side of the equation.
-0.9921875 + 0.9921875 + v = -0.92705773 + 0.9921875

Combine like terms: -0.9921875 + 0.9921875 = 0.0000000
0.0000000 + v = -0.92705773 + 0.9921875
v = -0.92705773 + 0.9921875

Combine like terms: -0.92705773 + 0.9921875 = 0.06512977
v = 0.06512977

Simplifying
v = 0.06512977

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {1.91924523, 0.06512977}
Solution
v = {1.91924523, 0.06512977}