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

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

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

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

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

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

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

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

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

Combine like terms: 5v + 2v = 7v
2 + 7v + -1v2 + 7v2 = 0

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

Solving
2 + 7v + 6v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(2 + 3v)(1 + 2v) = 0

Subproblem 1
Set the factor '(2 + 3v)' equal to zero and attempt to solve:

Simplifying
2 + 3v = 0

Solving
2 + 3v = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3v = 0 + -2
3v = 0 + -2

Combine like terms: 0 + -2 = -2
3v = -2

Divide each side by '3'.
v = -0.6666666667

Simplifying
v = -0.6666666667
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 = {-0.6666666667, -0.5}