w^2+5w+6=0

Solution for w^2+5w+6=0 equation:

Simplifying
w2 + 5w + 6 = 0

Reorder the terms:
6 + 5w + w2 = 0

Solving
6 + 5w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(3 + w)(2 + w) = 0

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

Simplifying
3 + w = 0

Solving
3 + w = 0

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

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

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

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

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

Simplifying
2 + w = 0

Solving
2 + w = 0

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

Add '-2' to each side of the equation.
2 + -2 + w = 0 + -2

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

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

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