8(v+4)2v=3(2v+2)-11

Solution for 8(v+4)2v=3(2v+2)-11 equation:

Simplifying
8(v + 4) * 2v = 3(2v + 2) + -11

Reorder the terms:
8(4 + v) * 2v = 3(2v + 2) + -11

Reorder the terms for easier multiplication:
8 * 2v(4 + v) = 3(2v + 2) + -11

Multiply 8 * 2
16v(4 + v) = 3(2v + 2) + -11
(4 * 16v + v * 16v) = 3(2v + 2) + -11
(64v + 16v2) = 3(2v + 2) + -11

Reorder the terms:
64v + 16v2 = 3(2 + 2v) + -11
64v + 16v2 = (2 * 3 + 2v * 3) + -11
64v + 16v2 = (6 + 6v) + -11

Reorder the terms:
64v + 16v2 = 6 + -11 + 6v

Combine like terms: 6 + -11 = -5
64v + 16v2 = -5 + 6v

Solving
64v + 16v2 = -5 + 6v

Solving for variable 'v'.

Reorder the terms:
5 + 64v + -6v + 16v2 = -5 + 6v + 5 + -6v

Combine like terms: 64v + -6v = 58v
5 + 58v + 16v2 = -5 + 6v + 5 + -6v

Reorder the terms:
5 + 58v + 16v2 = -5 + 5 + 6v + -6v

Combine like terms: -5 + 5 = 0
5 + 58v + 16v2 = 0 + 6v + -6v
5 + 58v + 16v2 = 6v + -6v

Combine like terms: 6v + -6v = 0
5 + 58v + 16v2 = 0

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

Divide each side by '16'.
0.3125 + 3.625v + v2 = 0

Move the constant term to the right:

Add '-0.3125' to each side of the equation.
0.3125 + 3.625v + -0.3125 + v2 = 0 + -0.3125

Reorder the terms:
0.3125 + -0.3125 + 3.625v + v2 = 0 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + 3.625v + v2 = 0 + -0.3125
3.625v + v2 = 0 + -0.3125

Combine like terms: 0 + -0.3125 = -0.3125
3.625v + v2 = -0.3125

The v term is 3.625v.  Take half its coefficient (1.8125).
Square it (3.28515625) and add it to both sides.

Add '3.28515625' to each side of the equation.
3.625v + 3.28515625 + v2 = -0.3125 + 3.28515625

Reorder the terms:
3.28515625 + 3.625v + v2 = -0.3125 + 3.28515625

Combine like terms: -0.3125 + 3.28515625 = 2.97265625
3.28515625 + 3.625v + v2 = 2.97265625

Factor a perfect square on the left side:
(v + 1.8125)(v + 1.8125) = 2.97265625

Calculate the square root of the right side: 1.724139278

Break this problem into two subproblems by setting 
(v + 1.8125) equal to 1.724139278 and -1.724139278.

Subproblem 1
v + 1.8125 = 1.724139278

Simplifying
v + 1.8125 = 1.724139278

Reorder the terms:
1.8125 + v = 1.724139278

Solving
1.8125 + v = 1.724139278

Solving for variable 'v'.

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

Add '-1.8125' to each side of the equation.
1.8125 + -1.8125 + v = 1.724139278 + -1.8125

Combine like terms: 1.8125 + -1.8125 = 0.0000
0.0000 + v = 1.724139278 + -1.8125
v = 1.724139278 + -1.8125

Combine like terms: 1.724139278 + -1.8125 = -0.088360722
v = -0.088360722

Simplifying
v = -0.088360722

Subproblem 2
v + 1.8125 = -1.724139278

Simplifying
v + 1.8125 = -1.724139278

Reorder the terms:
1.8125 + v = -1.724139278

Solving
1.8125 + v = -1.724139278

Solving for variable 'v'.

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

Add '-1.8125' to each side of the equation.
1.8125 + -1.8125 + v = -1.724139278 + -1.8125

Combine like terms: 1.8125 + -1.8125 = 0.0000
0.0000 + v = -1.724139278 + -1.8125
v = -1.724139278 + -1.8125

Combine like terms: -1.724139278 + -1.8125 = -3.536639278
v = -3.536639278

Simplifying
v = -3.536639278

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-0.088360722, -3.536639278}