(-9v^2-9v+6)+(4v^2-2v+1)-(3v^2-8v-8)=

Solution for (-9v^2-9v+6)+(4v^2-2v+1)-(3v^2-8v-8)= equation:

Simplifying
(-9v2 + -9v + 6) + (4v2 + -2v + 1) + -1(3v2 + -8v + -8) = 0

Reorder the terms:
(6 + -9v + -9v2) + (4v2 + -2v + 1) + -1(3v2 + -8v + -8) = 0

Remove parenthesis around (6 + -9v + -9v2)
6 + -9v + -9v2 + (4v2 + -2v + 1) + -1(3v2 + -8v + -8) = 0

Reorder the terms:
6 + -9v + -9v2 + (1 + -2v + 4v2) + -1(3v2 + -8v + -8) = 0

Remove parenthesis around (1 + -2v + 4v2)
6 + -9v + -9v2 + 1 + -2v + 4v2 + -1(3v2 + -8v + -8) = 0

Reorder the terms:
6 + -9v + -9v2 + 1 + -2v + 4v2 + -1(-8 + -8v + 3v2) = 0
6 + -9v + -9v2 + 1 + -2v + 4v2 + (-8 * -1 + -8v * -1 + 3v2 * -1) = 0
6 + -9v + -9v2 + 1 + -2v + 4v2 + (8 + 8v + -3v2) = 0

Reorder the terms:
6 + 1 + 8 + -9v + -2v + 8v + -9v2 + 4v2 + -3v2 = 0

Combine like terms: 6 + 1 = 7
7 + 8 + -9v + -2v + 8v + -9v2 + 4v2 + -3v2 = 0

Combine like terms: 7 + 8 = 15
15 + -9v + -2v + 8v + -9v2 + 4v2 + -3v2 = 0

Combine like terms: -9v + -2v = -11v
15 + -11v + 8v + -9v2 + 4v2 + -3v2 = 0

Combine like terms: -11v + 8v = -3v
15 + -3v + -9v2 + 4v2 + -3v2 = 0

Combine like terms: -9v2 + 4v2 = -5v2
15 + -3v + -5v2 + -3v2 = 0

Combine like terms: -5v2 + -3v2 = -8v2
15 + -3v + -8v2 = 0

Solving
15 + -3v + -8v2 = 0

Solving for variable 'v'.

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-1.875 + 0.375v + v2 = 0

Move the constant term to the right:

Add '1.875' to each side of the equation.
-1.875 + 0.375v + 1.875 + v2 = 0 + 1.875

Reorder the terms:
-1.875 + 1.875 + 0.375v + v2 = 0 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + 0.375v + v2 = 0 + 1.875
0.375v + v2 = 0 + 1.875

Combine like terms: 0 + 1.875 = 1.875
0.375v + v2 = 1.875

The v term is 0.375v.  Take half its coefficient (0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
0.375v + 0.03515625 + v2 = 1.875 + 0.03515625

Reorder the terms:
0.03515625 + 0.375v + v2 = 1.875 + 0.03515625

Combine like terms: 1.875 + 0.03515625 = 1.91015625
0.03515625 + 0.375v + v2 = 1.91015625

Factor a perfect square on the left side:
(v + 0.1875)(v + 0.1875) = 1.91015625

Calculate the square root of the right side: 1.382084024

Break this problem into two subproblems by setting 
(v + 0.1875) equal to 1.382084024 and -1.382084024.

Subproblem 1
v + 0.1875 = 1.382084024

Simplifying
v + 0.1875 = 1.382084024

Reorder the terms:
0.1875 + v = 1.382084024

Solving
0.1875 + v = 1.382084024

Solving for variable 'v'.

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

Add '-0.1875' to each side of the equation.
0.1875 + -0.1875 + v = 1.382084024 + -0.1875

Combine like terms: 0.1875 + -0.1875 = 0.0000
0.0000 + v = 1.382084024 + -0.1875
v = 1.382084024 + -0.1875

Combine like terms: 1.382084024 + -0.1875 = 1.194584024
v = 1.194584024

Simplifying
v = 1.194584024

Subproblem 2
v + 0.1875 = -1.382084024

Simplifying
v + 0.1875 = -1.382084024

Reorder the terms:
0.1875 + v = -1.382084024

Solving
0.1875 + v = -1.382084024

Solving for variable 'v'.

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

Add '-0.1875' to each side of the equation.
0.1875 + -0.1875 + v = -1.382084024 + -0.1875

Combine like terms: 0.1875 + -0.1875 = 0.0000
0.0000 + v = -1.382084024 + -0.1875
v = -1.382084024 + -0.1875

Combine like terms: -1.382084024 + -0.1875 = -1.569584024
v = -1.569584024

Simplifying
v = -1.569584024

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {1.194584024, -1.569584024}