v^2+5v=-6

Solution for v^2+5v=-6 equation:

Simplifying
v2 + 5v = -6

Reorder the terms:
5v + v2 = -6

Solving
5v + v2 = -6

Solving for variable 'v'.

Reorder the terms:
6 + 5v + v2 = -6 + 6

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

Factor a trinomial.
(3 + v)(2 + 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 '(2 + v)' equal to zero and attempt to solve:

Simplifying
2 + v = 0

Solving
2 + v = 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 + v = 0 + -2

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

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

Simplifying
v = -2
Solution
v = {-3, -2}