0=-m^2+15m-54

Solution for 0=-m^2+15m-54 equation:

Simplifying
0 = -1m2 + 15m + -54

Reorder the terms:
0 = -54 + 15m + -1m2

Solving
0 = -54 + 15m + -1m2

Solving for variable 'm'.

Combine like terms: 0 + 54 = 54
54 + -15m + m2 = -54 + 15m + -1m2 + 54 + -15m + m2

Reorder the terms:
54 + -15m + m2 = -54 + 54 + 15m + -15m + -1m2 + m2

Combine like terms: -54 + 54 = 0
54 + -15m + m2 = 0 + 15m + -15m + -1m2 + m2
54 + -15m + m2 = 15m + -15m + -1m2 + m2

Combine like terms: 15m + -15m = 0
54 + -15m + m2 = 0 + -1m2 + m2
54 + -15m + m2 = -1m2 + m2

Combine like terms: -1m2 + m2 = 0
54 + -15m + m2 = 0

Factor a trinomial.
(6 + -1m)(9 + -1m) = 0

Subproblem 1
Set the factor '(6 + -1m)' equal to zero and attempt to solve:

Simplifying
6 + -1m = 0

Solving
6 + -1m = 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 + -1m = 0 + -6

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

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

Divide each side by '-1'.
m = 6

Simplifying
m = 6
Subproblem 2
Set the factor '(9 + -1m)' equal to zero and attempt to solve:

Simplifying
9 + -1m = 0

Solving
9 + -1m = 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 + -1m = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1m = 0 + -9
-1m = 0 + -9

Combine like terms: 0 + -9 = -9
-1m = -9

Divide each side by '-1'.
m = 9

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