(9v^2+5v+2)+(5v^2+4v-3)-(3v^2+7v+9)=0

Solution for (9v^2+5v+2)+(5v^2+4v-3)-(3v^2+7v+9)=0 equation:

Simplifying
(9v2 + 5v + 2) + (5v2 + 4v + -3) + -1(3v2 + 7v + 9) = 0

Reorder the terms:
(2 + 5v + 9v2) + (5v2 + 4v + -3) + -1(3v2 + 7v + 9) = 0

Remove parenthesis around (2 + 5v + 9v2)
2 + 5v + 9v2 + (5v2 + 4v + -3) + -1(3v2 + 7v + 9) = 0

Reorder the terms:
2 + 5v + 9v2 + (-3 + 4v + 5v2) + -1(3v2 + 7v + 9) = 0

Remove parenthesis around (-3 + 4v + 5v2)
2 + 5v + 9v2 + -3 + 4v + 5v2 + -1(3v2 + 7v + 9) = 0

Reorder the terms:
2 + 5v + 9v2 + -3 + 4v + 5v2 + -1(9 + 7v + 3v2) = 0
2 + 5v + 9v2 + -3 + 4v + 5v2 + (9 * -1 + 7v * -1 + 3v2 * -1) = 0
2 + 5v + 9v2 + -3 + 4v + 5v2 + (-9 + -7v + -3v2) = 0

Reorder the terms:
2 + -3 + -9 + 5v + 4v + -7v + 9v2 + 5v2 + -3v2 = 0

Combine like terms: 2 + -3 = -1
-1 + -9 + 5v + 4v + -7v + 9v2 + 5v2 + -3v2 = 0

Combine like terms: -1 + -9 = -10
-10 + 5v + 4v + -7v + 9v2 + 5v2 + -3v2 = 0

Combine like terms: 5v + 4v = 9v
-10 + 9v + -7v + 9v2 + 5v2 + -3v2 = 0

Combine like terms: 9v + -7v = 2v
-10 + 2v + 9v2 + 5v2 + -3v2 = 0

Combine like terms: 9v2 + 5v2 = 14v2
-10 + 2v + 14v2 + -3v2 = 0

Combine like terms: 14v2 + -3v2 = 11v2
-10 + 2v + 11v2 = 0

Solving
-10 + 2v + 11v2 = 0

Solving for variable 'v'.

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

Divide each side by '11'.
-0.9090909091 + 0.1818181818v + v2 = 0

Move the constant term to the right:

Add '0.9090909091' to each side of the equation.
-0.9090909091 + 0.1818181818v + 0.9090909091 + v2 = 0 + 0.9090909091

Reorder the terms:
-0.9090909091 + 0.9090909091 + 0.1818181818v + v2 = 0 + 0.9090909091

Combine like terms: -0.9090909091 + 0.9090909091 = 0.0000000000
0.0000000000 + 0.1818181818v + v2 = 0 + 0.9090909091
0.1818181818v + v2 = 0 + 0.9090909091

Combine like terms: 0 + 0.9090909091 = 0.9090909091
0.1818181818v + v2 = 0.9090909091

The v term is 0.1818181818v.  Take half its coefficient (0.0909090909).
Square it (0.008264462808) and add it to both sides.

Add '0.008264462808' to each side of the equation.
0.1818181818v + 0.008264462808 + v2 = 0.9090909091 + 0.008264462808

Reorder the terms:
0.008264462808 + 0.1818181818v + v2 = 0.9090909091 + 0.008264462808

Combine like terms: 0.9090909091 + 0.008264462808 = 0.917355371908
0.008264462808 + 0.1818181818v + v2 = 0.917355371908

Factor a perfect square on the left side:
(v + 0.0909090909)(v + 0.0909090909) = 0.917355371908

Calculate the square root of the right side: 0.957786705

Break this problem into two subproblems by setting 
(v + 0.0909090909) equal to 0.957786705 and -0.957786705.

Subproblem 1
v + 0.0909090909 = 0.957786705

Simplifying
v + 0.0909090909 = 0.957786705

Reorder the terms:
0.0909090909 + v = 0.957786705

Solving
0.0909090909 + v = 0.957786705

Solving for variable 'v'.

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

Add '-0.0909090909' to each side of the equation.
0.0909090909 + -0.0909090909 + v = 0.957786705 + -0.0909090909

Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000
0.0000000000 + v = 0.957786705 + -0.0909090909
v = 0.957786705 + -0.0909090909

Combine like terms: 0.957786705 + -0.0909090909 = 0.8668776141
v = 0.8668776141

Simplifying
v = 0.8668776141

Subproblem 2
v + 0.0909090909 = -0.957786705

Simplifying
v + 0.0909090909 = -0.957786705

Reorder the terms:
0.0909090909 + v = -0.957786705

Solving
0.0909090909 + v = -0.957786705

Solving for variable 'v'.

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

Add '-0.0909090909' to each side of the equation.
0.0909090909 + -0.0909090909 + v = -0.957786705 + -0.0909090909

Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000
0.0000000000 + v = -0.957786705 + -0.0909090909
v = -0.957786705 + -0.0909090909

Combine like terms: -0.957786705 + -0.0909090909 = -1.0486957959
v = -1.0486957959

Simplifying
v = -1.0486957959

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {0.8668776141, -1.0486957959}