16v(v+4)-4v=3(4v+4)-20

Solution for 16v(v+4)-4v=3(4v+4)-20 equation:

Simplifying
16v(v + 4) + -4v = 3(4v + 4) + -20

Reorder the terms:
16v(4 + v) + -4v = 3(4v + 4) + -20
(4 * 16v + v * 16v) + -4v = 3(4v + 4) + -20
(64v + 16v2) + -4v = 3(4v + 4) + -20

Reorder the terms:
64v + -4v + 16v2 = 3(4v + 4) + -20

Combine like terms: 64v + -4v = 60v
60v + 16v2 = 3(4v + 4) + -20

Reorder the terms:
60v + 16v2 = 3(4 + 4v) + -20
60v + 16v2 = (4 * 3 + 4v * 3) + -20
60v + 16v2 = (12 + 12v) + -20

Reorder the terms:
60v + 16v2 = 12 + -20 + 12v

Combine like terms: 12 + -20 = -8
60v + 16v2 = -8 + 12v

Solving
60v + 16v2 = -8 + 12v

Solving for variable 'v'.

Reorder the terms:
8 + 60v + -12v + 16v2 = -8 + 12v + 8 + -12v

Combine like terms: 60v + -12v = 48v
8 + 48v + 16v2 = -8 + 12v + 8 + -12v

Reorder the terms:
8 + 48v + 16v2 = -8 + 8 + 12v + -12v

Combine like terms: -8 + 8 = 0
8 + 48v + 16v2 = 0 + 12v + -12v
8 + 48v + 16v2 = 12v + -12v

Combine like terms: 12v + -12v = 0
8 + 48v + 16v2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(1 + 6v + 2v2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(1 + 6v + 2v2)' equal to zero and attempt to solve:

Simplifying
1 + 6v + 2v2 = 0

Solving
1 + 6v + 2v2 = 0

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

Divide each side by '2'.
0.5 + 3v + v2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 3v + -0.5 + v2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 3v + v2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 3v + v2 = 0 + -0.5
3v + v2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
3v + v2 = -0.5

The v term is 3v.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3v + 2.25 + v2 = -0.5 + 2.25

Reorder the terms:
2.25 + 3v + v2 = -0.5 + 2.25

Combine like terms: -0.5 + 2.25 = 1.75
2.25 + 3v + v2 = 1.75

Factor a perfect square on the left side:
(v + 1.5)(v + 1.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(v + 1.5) equal to 1.322875656 and -1.322875656.

Subproblem 1
v + 1.5 = 1.322875656

Simplifying
v + 1.5 = 1.322875656

Reorder the terms:
1.5 + v = 1.322875656

Solving
1.5 + v = 1.322875656

Solving for variable 'v'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + v = 1.322875656 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + v = 1.322875656 + -1.5
v = 1.322875656 + -1.5

Combine like terms: 1.322875656 + -1.5 = -0.177124344
v = -0.177124344

Simplifying
v = -0.177124344

Subproblem 2
v + 1.5 = -1.322875656

Simplifying
v + 1.5 = -1.322875656

Reorder the terms:
1.5 + v = -1.322875656

Solving
1.5 + v = -1.322875656

Solving for variable 'v'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + v = -1.322875656 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + v = -1.322875656 + -1.5
v = -1.322875656 + -1.5

Combine like terms: -1.322875656 + -1.5 = -2.822875656
v = -2.822875656

Simplifying
v = -2.822875656

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-0.177124344, -2.822875656}
Solution
v = {-0.177124344, -2.822875656}