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

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

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

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

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

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

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

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

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

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

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

Solving
4 + 7v + -2v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(4 + -1v)(1 + 2v) = 0

Subproblem 1
Set the factor '(4 + -1v)' equal to zero and attempt to solve:

Simplifying
4 + -1v = 0

Solving
4 + -1v = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1v = 0 + -4
-1v = 0 + -4

Combine like terms: 0 + -4 = -4
-1v = -4

Divide each side by '-1'.
v = 4

Simplifying
v = 4
Subproblem 2
Set the factor '(1 + 2v)' equal to zero and attempt to solve:

Simplifying
1 + 2v = 0

Solving
1 + 2v = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2v = 0 + -1
2v = 0 + -1

Combine like terms: 0 + -1 = -1
2v = -1

Divide each side by '2'.
v = -0.5

Simplifying
v = -0.5
Solution
v = {4, -0.5}