b^2+5b+6=0

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

Simplifying
b2 + 5b + 6 = 0

Reorder the terms:
6 + 5b + b2 = 0

Solving
6 + 5b + b2 = 0

Solving for variable 'b'.

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

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

Simplifying
3 + b = 0

Solving
3 + b = 0

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

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

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

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

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

Simplifying
2 + b = 0

Solving
2 + b = 0

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

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

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

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

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