v^2+6v+18=-3v

Solution for v^2+6v+18=-3v equation:

Simplifying
v2 + 6v + 18 = -3v

Reorder the terms:
18 + 6v + v2 = -3v

Solving
18 + 6v + v2 = -3v

Solving for variable 'v'.

Reorder the terms:
18 + 6v + 3v + v2 = -3v + 3v

Combine like terms: 6v + 3v = 9v
18 + 9v + v2 = -3v + 3v

Combine like terms: -3v + 3v = 0
18 + 9v + v2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
v = {-6, -3}