v^2+6v+9=0

Solution for v^2+6v+9=0 equation:

Simplifying
v2 + 6v + 9 = 0

Reorder the terms:
9 + 6v + v2 = 0

Solving
9 + 6v + v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(3 + v)(3 + 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 '(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 = {-3, -3}