0=5+6m+m^2

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

Simplifying
0 = 5 + 6m + m2

Solving
0 = 5 + 6m + m2

Solving for variable 'm'.

Combine like terms: 0 + -5 = -5
-5 + -6m + -1m2 = 5 + 6m + m2 + -5 + -6m + -1m2

Reorder the terms:
-5 + -6m + -1m2 = 5 + -5 + 6m + -6m + m2 + -1m2

Combine like terms: 5 + -5 = 0
-5 + -6m + -1m2 = 0 + 6m + -6m + m2 + -1m2
-5 + -6m + -1m2 = 6m + -6m + m2 + -1m2

Combine like terms: 6m + -6m = 0
-5 + -6m + -1m2 = 0 + m2 + -1m2
-5 + -6m + -1m2 = m2 + -1m2

Combine like terms: m2 + -1m2 = 0
-5 + -6m + -1m2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 6m + m2) = 0

Factor a trinomial.
-1((5 + m)(1 + m)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(5 + m)' equal to zero and attempt to solve:

Simplifying
5 + m = 0

Solving
5 + m = 0

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

Add '-5' to each side of the equation.
5 + -5 + m = 0 + -5

Combine like terms: 5 + -5 = 0
0 + m = 0 + -5
m = 0 + -5

Combine like terms: 0 + -5 = -5
m = -5

Simplifying
m = -5
Subproblem 2
Set the factor '(1 + m)' equal to zero and attempt to solve:

Simplifying
1 + m = 0

Solving
1 + m = 0

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

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

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

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

Simplifying
m = -1
Solution
m = {-5, -1}