(2v^2+9v-8)-(-8v^2+6v+7)+(9v^2-7v+1)=

Solution for (2v^2+9v-8)-(-8v^2+6v+7)+(9v^2-7v+1)= equation:

Simplifying
(2v2 + 9v + -8) + -1(-8v2 + 6v + 7) + (9v2 + -7v + 1) = 0

Reorder the terms:
(-8 + 9v + 2v2) + -1(-8v2 + 6v + 7) + (9v2 + -7v + 1) = 0

Remove parenthesis around (-8 + 9v + 2v2)
-8 + 9v + 2v2 + -1(-8v2 + 6v + 7) + (9v2 + -7v + 1) = 0

Reorder the terms:
-8 + 9v + 2v2 + -1(7 + 6v + -8v2) + (9v2 + -7v + 1) = 0
-8 + 9v + 2v2 + (7 * -1 + 6v * -1 + -8v2 * -1) + (9v2 + -7v + 1) = 0
-8 + 9v + 2v2 + (-7 + -6v + 8v2) + (9v2 + -7v + 1) = 0

Reorder the terms:
-8 + 9v + 2v2 + -7 + -6v + 8v2 + (1 + -7v + 9v2) = 0

Remove parenthesis around (1 + -7v + 9v2)
-8 + 9v + 2v2 + -7 + -6v + 8v2 + 1 + -7v + 9v2 = 0

Reorder the terms:
-8 + -7 + 1 + 9v + -6v + -7v + 2v2 + 8v2 + 9v2 = 0

Combine like terms: -8 + -7 = -15
-15 + 1 + 9v + -6v + -7v + 2v2 + 8v2 + 9v2 = 0

Combine like terms: -15 + 1 = -14
-14 + 9v + -6v + -7v + 2v2 + 8v2 + 9v2 = 0

Combine like terms: 9v + -6v = 3v
-14 + 3v + -7v + 2v2 + 8v2 + 9v2 = 0

Combine like terms: 3v + -7v = -4v
-14 + -4v + 2v2 + 8v2 + 9v2 = 0

Combine like terms: 2v2 + 8v2 = 10v2
-14 + -4v + 10v2 + 9v2 = 0

Combine like terms: 10v2 + 9v2 = 19v2
-14 + -4v + 19v2 = 0

Solving
-14 + -4v + 19v2 = 0

Solving for variable 'v'.

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

Divide each side by '19'.
-0.7368421053 + -0.2105263158v + v2 = 0

Move the constant term to the right:

Add '0.7368421053' to each side of the equation.
-0.7368421053 + -0.2105263158v + 0.7368421053 + v2 = 0 + 0.7368421053

Reorder the terms:
-0.7368421053 + 0.7368421053 + -0.2105263158v + v2 = 0 + 0.7368421053

Combine like terms: -0.7368421053 + 0.7368421053 = 0.0000000000
0.0000000000 + -0.2105263158v + v2 = 0 + 0.7368421053
-0.2105263158v + v2 = 0 + 0.7368421053

Combine like terms: 0 + 0.7368421053 = 0.7368421053
-0.2105263158v + v2 = 0.7368421053

The v term is -0.2105263158v.  Take half its coefficient (-0.1052631579).
Square it (0.01108033241) and add it to both sides.

Add '0.01108033241' to each side of the equation.
-0.2105263158v + 0.01108033241 + v2 = 0.7368421053 + 0.01108033241

Reorder the terms:
0.01108033241 + -0.2105263158v + v2 = 0.7368421053 + 0.01108033241

Combine like terms: 0.7368421053 + 0.01108033241 = 0.74792243771
0.01108033241 + -0.2105263158v + v2 = 0.74792243771

Factor a perfect square on the left side:
(v + -0.1052631579)(v + -0.1052631579) = 0.74792243771

Calculate the square root of the right side: 0.864825091

Break this problem into two subproblems by setting 
(v + -0.1052631579) equal to 0.864825091 and -0.864825091.

Subproblem 1
v + -0.1052631579 = 0.864825091

Simplifying
v + -0.1052631579 = 0.864825091

Reorder the terms:
-0.1052631579 + v = 0.864825091

Solving
-0.1052631579 + v = 0.864825091

Solving for variable 'v'.

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

Add '0.1052631579' to each side of the equation.
-0.1052631579 + 0.1052631579 + v = 0.864825091 + 0.1052631579

Combine like terms: -0.1052631579 + 0.1052631579 = 0.0000000000
0.0000000000 + v = 0.864825091 + 0.1052631579
v = 0.864825091 + 0.1052631579

Combine like terms: 0.864825091 + 0.1052631579 = 0.9700882489
v = 0.9700882489

Simplifying
v = 0.9700882489

Subproblem 2
v + -0.1052631579 = -0.864825091

Simplifying
v + -0.1052631579 = -0.864825091

Reorder the terms:
-0.1052631579 + v = -0.864825091

Solving
-0.1052631579 + v = -0.864825091

Solving for variable 'v'.

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

Add '0.1052631579' to each side of the equation.
-0.1052631579 + 0.1052631579 + v = -0.864825091 + 0.1052631579

Combine like terms: -0.1052631579 + 0.1052631579 = 0.0000000000
0.0000000000 + v = -0.864825091 + 0.1052631579
v = -0.864825091 + 0.1052631579

Combine like terms: -0.864825091 + 0.1052631579 = -0.7595619331
v = -0.7595619331

Simplifying
v = -0.7595619331

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {0.9700882489, -0.7595619331}