b^2+5b+b=0

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

Simplifying
b2 + 5b + b = 0

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

Combine like terms: 5b + b = 6b
6b + b2 = 0

Solving
6b + b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), 'b'.
b(6 + b) = 0

Subproblem 1
Set the factor 'b' equal to zero and attempt to solve:

Simplifying
b = 0

Solving
b = 0

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

Simplifying
b = 0
Subproblem 2
Set the factor '(6 + b)' equal to zero and attempt to solve:

Simplifying
6 + b = 0

Solving
6 + b = 0

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

Add '-6' to each side of the equation.
6 + -6 + b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + b = 0 + -6
b = 0 + -6

Combine like terms: 0 + -6 = -6
b = -6

Simplifying
b = -6
Solution
b = {0, -6}