-9v(v+2)+2v+6=5v+8

Solution for -9v(v+2)+2v+6=5v+8 equation:

Simplifying
-9v(v + 2) + 2v + 6 = 5v + 8

Reorder the terms:
-9v(2 + v) + 2v + 6 = 5v + 8
(2 * -9v + v * -9v) + 2v + 6 = 5v + 8
(-18v + -9v2) + 2v + 6 = 5v + 8

Reorder the terms:
6 + -18v + 2v + -9v2 = 5v + 8

Combine like terms: -18v + 2v = -16v
6 + -16v + -9v2 = 5v + 8

Reorder the terms:
6 + -16v + -9v2 = 8 + 5v

Solving
6 + -16v + -9v2 = 8 + 5v

Solving for variable 'v'.

Reorder the terms:
6 + -8 + -16v + -5v + -9v2 = 8 + 5v + -8 + -5v

Combine like terms: 6 + -8 = -2
-2 + -16v + -5v + -9v2 = 8 + 5v + -8 + -5v

Combine like terms: -16v + -5v = -21v
-2 + -21v + -9v2 = 8 + 5v + -8 + -5v

Reorder the terms:
-2 + -21v + -9v2 = 8 + -8 + 5v + -5v

Combine like terms: 8 + -8 = 0
-2 + -21v + -9v2 = 0 + 5v + -5v
-2 + -21v + -9v2 = 5v + -5v

Combine like terms: 5v + -5v = 0
-2 + -21v + -9v2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 21v + 9v2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(2 + 21v + 9v2)' equal to zero and attempt to solve:

Simplifying
2 + 21v + 9v2 = 0

Solving
2 + 21v + 9v2 = 0

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

Divide each side by '9'.
0.2222222222 + 2.333333333v + v2 = 0

Move the constant term to the right:

Add '-0.2222222222' to each side of the equation.
0.2222222222 + 2.333333333v + -0.2222222222 + v2 = 0 + -0.2222222222

Reorder the terms:
0.2222222222 + -0.2222222222 + 2.333333333v + v2 = 0 + -0.2222222222

Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000
0.0000000000 + 2.333333333v + v2 = 0 + -0.2222222222
2.333333333v + v2 = 0 + -0.2222222222

Combine like terms: 0 + -0.2222222222 = -0.2222222222
2.333333333v + v2 = -0.2222222222

The v term is 2.333333333v.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333v + 1.361111112 + v2 = -0.2222222222 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333v + v2 = -0.2222222222 + 1.361111112

Combine like terms: -0.2222222222 + 1.361111112 = 1.1388888898
1.361111112 + 2.333333333v + v2 = 1.1388888898

Factor a perfect square on the left side:
(v + 1.166666667)(v + 1.166666667) = 1.1388888898

Calculate the square root of the right side: 1.067187373

Break this problem into two subproblems by setting 
(v + 1.166666667) equal to 1.067187373 and -1.067187373.

Subproblem 1
v + 1.166666667 = 1.067187373

Simplifying
v + 1.166666667 = 1.067187373

Reorder the terms:
1.166666667 + v = 1.067187373

Solving
1.166666667 + v = 1.067187373

Solving for variable 'v'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + v = 1.067187373 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + v = 1.067187373 + -1.166666667
v = 1.067187373 + -1.166666667

Combine like terms: 1.067187373 + -1.166666667 = -0.099479294
v = -0.099479294

Simplifying
v = -0.099479294

Subproblem 2
v + 1.166666667 = -1.067187373

Simplifying
v + 1.166666667 = -1.067187373

Reorder the terms:
1.166666667 + v = -1.067187373

Solving
1.166666667 + v = -1.067187373

Solving for variable 'v'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + v = -1.067187373 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + v = -1.067187373 + -1.166666667
v = -1.067187373 + -1.166666667

Combine like terms: -1.067187373 + -1.166666667 = -2.23385404
v = -2.23385404

Simplifying
v = -2.23385404

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-0.099479294, -2.23385404}
Solution
v = {-0.099479294, -2.23385404}