(4v^2+2v-1)+(-6v^2+3v+9)-(5v^2+7v-3)=

Solution for (4v^2+2v-1)+(-6v^2+3v+9)-(5v^2+7v-3)= equation:

Simplifying
(4v2 + 2v + -1) + (-6v2 + 3v + 9) + -1(5v2 + 7v + -3) = 0

Reorder the terms:
(-1 + 2v + 4v2) + (-6v2 + 3v + 9) + -1(5v2 + 7v + -3) = 0

Remove parenthesis around (-1 + 2v + 4v2)
-1 + 2v + 4v2 + (-6v2 + 3v + 9) + -1(5v2 + 7v + -3) = 0

Reorder the terms:
-1 + 2v + 4v2 + (9 + 3v + -6v2) + -1(5v2 + 7v + -3) = 0

Remove parenthesis around (9 + 3v + -6v2)
-1 + 2v + 4v2 + 9 + 3v + -6v2 + -1(5v2 + 7v + -3) = 0

Reorder the terms:
-1 + 2v + 4v2 + 9 + 3v + -6v2 + -1(-3 + 7v + 5v2) = 0
-1 + 2v + 4v2 + 9 + 3v + -6v2 + (-3 * -1 + 7v * -1 + 5v2 * -1) = 0
-1 + 2v + 4v2 + 9 + 3v + -6v2 + (3 + -7v + -5v2) = 0

Reorder the terms:
-1 + 9 + 3 + 2v + 3v + -7v + 4v2 + -6v2 + -5v2 = 0

Combine like terms: -1 + 9 = 8
8 + 3 + 2v + 3v + -7v + 4v2 + -6v2 + -5v2 = 0

Combine like terms: 8 + 3 = 11
11 + 2v + 3v + -7v + 4v2 + -6v2 + -5v2 = 0

Combine like terms: 2v + 3v = 5v
11 + 5v + -7v + 4v2 + -6v2 + -5v2 = 0

Combine like terms: 5v + -7v = -2v
11 + -2v + 4v2 + -6v2 + -5v2 = 0

Combine like terms: 4v2 + -6v2 = -2v2
11 + -2v + -2v2 + -5v2 = 0

Combine like terms: -2v2 + -5v2 = -7v2
11 + -2v + -7v2 = 0

Solving
11 + -2v + -7v2 = 0

Solving for variable 'v'.

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-1.571428571 + 0.2857142857v + v2 = 0

Move the constant term to the right:

Add '1.571428571' to each side of the equation.
-1.571428571 + 0.2857142857v + 1.571428571 + v2 = 0 + 1.571428571

Reorder the terms:
-1.571428571 + 1.571428571 + 0.2857142857v + v2 = 0 + 1.571428571

Combine like terms: -1.571428571 + 1.571428571 = 0.000000000
0.000000000 + 0.2857142857v + v2 = 0 + 1.571428571
0.2857142857v + v2 = 0 + 1.571428571

Combine like terms: 0 + 1.571428571 = 1.571428571
0.2857142857v + v2 = 1.571428571

The v term is 0.2857142857v.  Take half its coefficient (0.1428571429).
Square it (0.02040816328) and add it to both sides.

Add '0.02040816328' to each side of the equation.
0.2857142857v + 0.02040816328 + v2 = 1.571428571 + 0.02040816328

Reorder the terms:
0.02040816328 + 0.2857142857v + v2 = 1.571428571 + 0.02040816328

Combine like terms: 1.571428571 + 0.02040816328 = 1.59183673428
0.02040816328 + 0.2857142857v + v2 = 1.59183673428

Factor a perfect square on the left side:
(v + 0.1428571429)(v + 0.1428571429) = 1.59183673428

Calculate the square root of the right side: 1.261680124

Break this problem into two subproblems by setting 
(v + 0.1428571429) equal to 1.261680124 and -1.261680124.

Subproblem 1
v + 0.1428571429 = 1.261680124

Simplifying
v + 0.1428571429 = 1.261680124

Reorder the terms:
0.1428571429 + v = 1.261680124

Solving
0.1428571429 + v = 1.261680124

Solving for variable 'v'.

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

Add '-0.1428571429' to each side of the equation.
0.1428571429 + -0.1428571429 + v = 1.261680124 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + v = 1.261680124 + -0.1428571429
v = 1.261680124 + -0.1428571429

Combine like terms: 1.261680124 + -0.1428571429 = 1.1188229811
v = 1.1188229811

Simplifying
v = 1.1188229811

Subproblem 2
v + 0.1428571429 = -1.261680124

Simplifying
v + 0.1428571429 = -1.261680124

Reorder the terms:
0.1428571429 + v = -1.261680124

Solving
0.1428571429 + v = -1.261680124

Solving for variable 'v'.

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

Add '-0.1428571429' to each side of the equation.
0.1428571429 + -0.1428571429 + v = -1.261680124 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + v = -1.261680124 + -0.1428571429
v = -1.261680124 + -0.1428571429

Combine like terms: -1.261680124 + -0.1428571429 = -1.4045372669
v = -1.4045372669

Simplifying
v = -1.4045372669

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {1.1188229811, -1.4045372669}