m^2=-15m-54

Solution for m^2=-15m-54 equation:

Simplifying
m2 = -15m + -54

Reorder the terms:
m2 = -54 + -15m

Solving
m2 = -54 + -15m

Solving for variable 'm'.

Reorder the terms:
54 + 15m + m2 = -54 + -15m + 54 + 15m

Reorder the terms:
54 + 15m + m2 = -54 + 54 + -15m + 15m

Combine like terms: -54 + 54 = 0
54 + 15m + m2 = 0 + -15m + 15m
54 + 15m + m2 = -15m + 15m

Combine like terms: -15m + 15m = 0
54 + 15m + m2 = 0

Factor a trinomial.
(9 + m)(6 + 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 '(6 + m)' equal to zero and attempt to solve:

Simplifying
6 + m = 0

Solving
6 + m = 0

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

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

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

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

Simplifying
m = -6
Solution
m = {-9, -6}