-9v(v+2)+4v+5=5v+10

Solution for -9v(v+2)+4v+5=5v+10 equation:

Simplifying
-9v(v + 2) + 4v + 5 = 5v + 10

Reorder the terms:
-9v(2 + v) + 4v + 5 = 5v + 10
(2 * -9v + v * -9v) + 4v + 5 = 5v + 10
(-18v + -9v2) + 4v + 5 = 5v + 10

Reorder the terms:
5 + -18v + 4v + -9v2 = 5v + 10

Combine like terms: -18v + 4v = -14v
5 + -14v + -9v2 = 5v + 10

Reorder the terms:
5 + -14v + -9v2 = 10 + 5v

Solving
5 + -14v + -9v2 = 10 + 5v

Solving for variable 'v'.

Reorder the terms:
5 + -10 + -14v + -5v + -9v2 = 10 + 5v + -10 + -5v

Combine like terms: 5 + -10 = -5
-5 + -14v + -5v + -9v2 = 10 + 5v + -10 + -5v

Combine like terms: -14v + -5v = -19v
-5 + -19v + -9v2 = 10 + 5v + -10 + -5v

Reorder the terms:
-5 + -19v + -9v2 = 10 + -10 + 5v + -5v

Combine like terms: 10 + -10 = 0
-5 + -19v + -9v2 = 0 + 5v + -5v
-5 + -19v + -9v2 = 5v + -5v

Combine like terms: 5v + -5v = 0
-5 + -19v + -9v2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 19v + 9v2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(5 + 19v + 9v2)' equal to zero and attempt to solve:

Simplifying
5 + 19v + 9v2 = 0

Solving
5 + 19v + 9v2 = 0

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

Divide each side by '9'.
0.5555555556 + 2.111111111v + v2 = 0

Move the constant term to the right:

Add '-0.5555555556' to each side of the equation.
0.5555555556 + 2.111111111v + -0.5555555556 + v2 = 0 + -0.5555555556

Reorder the terms:
0.5555555556 + -0.5555555556 + 2.111111111v + v2 = 0 + -0.5555555556

Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000
0.0000000000 + 2.111111111v + v2 = 0 + -0.5555555556
2.111111111v + v2 = 0 + -0.5555555556

Combine like terms: 0 + -0.5555555556 = -0.5555555556
2.111111111v + v2 = -0.5555555556

The v term is 2.111111111v.  Take half its coefficient (1.055555556).
Square it (1.114197532) and add it to both sides.

Add '1.114197532' to each side of the equation.
2.111111111v + 1.114197532 + v2 = -0.5555555556 + 1.114197532

Reorder the terms:
1.114197532 + 2.111111111v + v2 = -0.5555555556 + 1.114197532

Combine like terms: -0.5555555556 + 1.114197532 = 0.5586419764
1.114197532 + 2.111111111v + v2 = 0.5586419764

Factor a perfect square on the left side:
(v + 1.055555556)(v + 1.055555556) = 0.5586419764

Calculate the square root of the right side: 0.747423559

Break this problem into two subproblems by setting 
(v + 1.055555556) equal to 0.747423559 and -0.747423559.

Subproblem 1
v + 1.055555556 = 0.747423559

Simplifying
v + 1.055555556 = 0.747423559

Reorder the terms:
1.055555556 + v = 0.747423559

Solving
1.055555556 + v = 0.747423559

Solving for variable 'v'.

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

Add '-1.055555556' to each side of the equation.
1.055555556 + -1.055555556 + v = 0.747423559 + -1.055555556

Combine like terms: 1.055555556 + -1.055555556 = 0.000000000
0.000000000 + v = 0.747423559 + -1.055555556
v = 0.747423559 + -1.055555556

Combine like terms: 0.747423559 + -1.055555556 = -0.308131997
v = -0.308131997

Simplifying
v = -0.308131997

Subproblem 2
v + 1.055555556 = -0.747423559

Simplifying
v + 1.055555556 = -0.747423559

Reorder the terms:
1.055555556 + v = -0.747423559

Solving
1.055555556 + v = -0.747423559

Solving for variable 'v'.

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

Add '-1.055555556' to each side of the equation.
1.055555556 + -1.055555556 + v = -0.747423559 + -1.055555556

Combine like terms: 1.055555556 + -1.055555556 = 0.000000000
0.000000000 + v = -0.747423559 + -1.055555556
v = -0.747423559 + -1.055555556

Combine like terms: -0.747423559 + -1.055555556 = -1.802979115
v = -1.802979115

Simplifying
v = -1.802979115

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-0.308131997, -1.802979115}
Solution
v = {-0.308131997, -1.802979115}