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

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

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

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

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

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

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

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

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

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

Combine like terms: -6v2 + 5v2 = -1v2
2 + 4v + -1v2 = 0

Solving
2 + 4v + -1v2 = 0

Solving for variable 'v'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2 + -4v + v2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -4v + 2 + v2 = 0 + 2

Reorder the terms:
-2 + 2 + -4v + v2 = 0 + 2

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

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

The v term is -4v.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4v + 4 + v2 = 2 + 4

Reorder the terms:
4 + -4v + v2 = 2 + 4

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

Factor a perfect square on the left side:
(v + -2)(v + -2) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(v + -2) equal to 2.449489743 and -2.449489743.

Subproblem 1
v + -2 = 2.449489743

Simplifying
v + -2 = 2.449489743

Reorder the terms:
-2 + v = 2.449489743

Solving
-2 + v = 2.449489743

Solving for variable 'v'.

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

Add '2' to each side of the equation.
-2 + 2 + v = 2.449489743 + 2

Combine like terms: -2 + 2 = 0
0 + v = 2.449489743 + 2
v = 2.449489743 + 2

Combine like terms: 2.449489743 + 2 = 4.449489743
v = 4.449489743

Simplifying
v = 4.449489743

Subproblem 2
v + -2 = -2.449489743

Simplifying
v + -2 = -2.449489743

Reorder the terms:
-2 + v = -2.449489743

Solving
-2 + v = -2.449489743

Solving for variable 'v'.

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

Add '2' to each side of the equation.
-2 + 2 + v = -2.449489743 + 2

Combine like terms: -2 + 2 = 0
0 + v = -2.449489743 + 2
v = -2.449489743 + 2

Combine like terms: -2.449489743 + 2 = -0.449489743
v = -0.449489743

Simplifying
v = -0.449489743

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {4.449489743, -0.449489743}