(b^2+3b)+b+3=0

Solution for (b^2+3b)+b+3=0 equation:

Simplifying
(b2 + 3b) + b + 3 = 0

Reorder the terms:
(3b + b2) + b + 3 = 0

Remove parenthesis around (3b + b2)
3b + b2 + b + 3 = 0

Reorder the terms:
3 + 3b + b + b2 = 0

Combine like terms: 3b + b = 4b
3 + 4b + b2 = 0

Solving
3 + 4b + b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(3 + b)(1 + 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 '(1 + b)' equal to zero and attempt to solve:

Simplifying
1 + b = 0

Solving
1 + b = 0

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

Add '-1' to each side of the equation.
1 + -1 + b = 0 + -1

Combine like terms: 1 + -1 = 0
0 + b = 0 + -1
b = 0 + -1

Combine like terms: 0 + -1 = -1
b = -1

Simplifying
b = -1
Solution
b = {-3, -1}