-v^2+14v-49+2v^2-10v+52=0

Solution for -v^2+14v-49+2v^2-10v+52=0 equation:

Simplifying
-1v2 + 14v + -49 + 2v2 + -10v + 52 = 0

Reorder the terms:
-49 + 52 + 14v + -10v + -1v2 + 2v2 = 0

Combine like terms: -49 + 52 = 3
3 + 14v + -10v + -1v2 + 2v2 = 0

Combine like terms: 14v + -10v = 4v
3 + 4v + -1v2 + 2v2 = 0

Combine like terms: -1v2 + 2v2 = 1v2
3 + 4v + 1v2 = 0

Solving
3 + 4v + 1v2 = 0

Solving for variable 'v'.

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

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

Simplifying
3 + v = 0

Solving
3 + v = 0

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

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

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

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

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

Simplifying
1 + v = 0

Solving
1 + v = 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 + v = 0 + -1

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

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

Simplifying
v = -1
Solution
v = {-3, -1}