-9(v+4)4v+5=8v+11

Solution for -9(v+4)4v+5=8v+11 equation:

Simplifying
-9(v + 4) * 4v + 5 = 8v + 11

Reorder the terms:
-9(4 + v) * 4v + 5 = 8v + 11

Reorder the terms for easier multiplication:
-9 * 4v(4 + v) + 5 = 8v + 11

Multiply -9 * 4
-36v(4 + v) + 5 = 8v + 11
(4 * -36v + v * -36v) + 5 = 8v + 11
(-144v + -36v2) + 5 = 8v + 11

Reorder the terms:
5 + -144v + -36v2 = 8v + 11

Reorder the terms:
5 + -144v + -36v2 = 11 + 8v

Solving
5 + -144v + -36v2 = 11 + 8v

Solving for variable 'v'.

Reorder the terms:
5 + -11 + -144v + -8v + -36v2 = 11 + 8v + -11 + -8v

Combine like terms: 5 + -11 = -6
-6 + -144v + -8v + -36v2 = 11 + 8v + -11 + -8v

Combine like terms: -144v + -8v = -152v
-6 + -152v + -36v2 = 11 + 8v + -11 + -8v

Reorder the terms:
-6 + -152v + -36v2 = 11 + -11 + 8v + -8v

Combine like terms: 11 + -11 = 0
-6 + -152v + -36v2 = 0 + 8v + -8v
-6 + -152v + -36v2 = 8v + -8v

Combine like terms: 8v + -8v = 0
-6 + -152v + -36v2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(3 + 76v + 18v2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(3 + 76v + 18v2)' equal to zero and attempt to solve:

Simplifying
3 + 76v + 18v2 = 0

Solving
3 + 76v + 18v2 = 0

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

Divide each side by '18'.
0.1666666667 + 4.222222222v + v2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + 4.222222222v + -0.1666666667 + v2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + 4.222222222v + v2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + 4.222222222v + v2 = 0 + -0.1666666667
4.222222222v + v2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
4.222222222v + v2 = -0.1666666667

The v term is 4.222222222v.  Take half its coefficient (2.111111111).
Square it (4.456790123) and add it to both sides.

Add '4.456790123' to each side of the equation.
4.222222222v + 4.456790123 + v2 = -0.1666666667 + 4.456790123

Reorder the terms:
4.456790123 + 4.222222222v + v2 = -0.1666666667 + 4.456790123

Combine like terms: -0.1666666667 + 4.456790123 = 4.2901234563
4.456790123 + 4.222222222v + v2 = 4.2901234563

Factor a perfect square on the left side:
(v + 2.111111111)(v + 2.111111111) = 4.2901234563

Calculate the square root of the right side: 2.07126132

Break this problem into two subproblems by setting 
(v + 2.111111111) equal to 2.07126132 and -2.07126132.

Subproblem 1
v + 2.111111111 = 2.07126132

Simplifying
v + 2.111111111 = 2.07126132

Reorder the terms:
2.111111111 + v = 2.07126132

Solving
2.111111111 + v = 2.07126132

Solving for variable 'v'.

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

Add '-2.111111111' to each side of the equation.
2.111111111 + -2.111111111 + v = 2.07126132 + -2.111111111

Combine like terms: 2.111111111 + -2.111111111 = 0.000000000
0.000000000 + v = 2.07126132 + -2.111111111
v = 2.07126132 + -2.111111111

Combine like terms: 2.07126132 + -2.111111111 = -0.039849791
v = -0.039849791

Simplifying
v = -0.039849791

Subproblem 2
v + 2.111111111 = -2.07126132

Simplifying
v + 2.111111111 = -2.07126132

Reorder the terms:
2.111111111 + v = -2.07126132

Solving
2.111111111 + v = -2.07126132

Solving for variable 'v'.

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

Add '-2.111111111' to each side of the equation.
2.111111111 + -2.111111111 + v = -2.07126132 + -2.111111111

Combine like terms: 2.111111111 + -2.111111111 = 0.000000000
0.000000000 + v = -2.07126132 + -2.111111111
v = -2.07126132 + -2.111111111

Combine like terms: -2.07126132 + -2.111111111 = -4.182372431
v = -4.182372431

Simplifying
v = -4.182372431

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-0.039849791, -4.182372431}
Solution
v = {-0.039849791, -4.182372431}