v^2=-42-13v

Solution for v^2=-42-13v equation:

Simplifying
v2 = -42 + -13v

Solving
v2 = -42 + -13v

Solving for variable 'v'.

Reorder the terms:
42 + 13v + v2 = -42 + -13v + 42 + 13v

Reorder the terms:
42 + 13v + v2 = -42 + 42 + -13v + 13v

Combine like terms: -42 + 42 = 0
42 + 13v + v2 = 0 + -13v + 13v
42 + 13v + v2 = -13v + 13v

Combine like terms: -13v + 13v = 0
42 + 13v + v2 = 0

Factor a trinomial.
(7 + v)(6 + v) = 0

Subproblem 1
Set the factor '(7 + v)' equal to zero and attempt to solve:

Simplifying
7 + v = 0

Solving
7 + v = 0

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

Add '-7' to each side of the equation.
7 + -7 + v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + v = 0 + -7
v = 0 + -7

Combine like terms: 0 + -7 = -7
v = -7

Simplifying
v = -7
Subproblem 2
Set the factor '(6 + v)' equal to zero and attempt to solve:

Simplifying
6 + v = 0

Solving
6 + v = 0

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

Add '-6' to each side of the equation.
6 + -6 + v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + v = 0 + -6
v = 0 + -6

Combine like terms: 0 + -6 = -6
v = -6

Simplifying
v = -6
Solution
v = {-7, -6}