Simplifying
m2 + 18m + 81 = 0

Reorder the terms:
81 + 18m + m2 = 0

Solving
81 + 18m + m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(9 + m)(9 + m) = 0

Subproblem 1
Set the factor '(9 + m)' equal to zero and attempt to solve:

Simplifying
9 + m = 0

Solving
9 + m = 0

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

Add '-9' to each side of the equation.
9 + -9 + m = 0 + -9

Combine like terms: 9 + -9 = 0
0 + m = 0 + -9
m = 0 + -9

Combine like terms: 0 + -9 = -9
m = -9

Simplifying
m = -9
Subproblem 2
Set the factor '(9 + m)' equal to zero and attempt to solve:

Simplifying
9 + m = 0

Solving
9 + m = 0

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

Add '-9' to each side of the equation.
9 + -9 + m = 0 + -9

Combine like terms: 9 + -9 = 0
0 + m = 0 + -9
m = 0 + -9

Combine like terms: 0 + -9 = -9
m = -9

Simplifying
m = -9
Solution
m = {-9, -9}