-m^2=14m-72

Solution for -m^2=14m-72 equation:

Simplifying
-1m2 = 14m + -72

Reorder the terms:
-1m2 = -72 + 14m

Solving
-1m2 = -72 + 14m

Solving for variable 'm'.

Reorder the terms:
72 + -14m + -1m2 = -72 + 14m + 72 + -14m

Reorder the terms:
72 + -14m + -1m2 = -72 + 72 + 14m + -14m

Combine like terms: -72 + 72 = 0
72 + -14m + -1m2 = 0 + 14m + -14m
72 + -14m + -1m2 = 14m + -14m

Combine like terms: 14m + -14m = 0
72 + -14m + -1m2 = 0

Factor a trinomial.
(4 + -1m)(18 + m) = 0

Subproblem 1
Set the factor '(4 + -1m)' equal to zero and attempt to solve:

Simplifying
4 + -1m = 0

Solving
4 + -1m = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1m = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1m = 0 + -4
-1m = 0 + -4

Combine like terms: 0 + -4 = -4
-1m = -4

Divide each side by '-1'.
m = 4

Simplifying
m = 4
Subproblem 2
Set the factor '(18 + m)' equal to zero and attempt to solve:

Simplifying
18 + m = 0

Solving
18 + m = 0

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

Add '-18' to each side of the equation.
18 + -18 + m = 0 + -18

Combine like terms: 18 + -18 = 0
0 + m = 0 + -18
m = 0 + -18

Combine like terms: 0 + -18 = -18
m = -18

Simplifying
m = -18
Solution
m = {4, -18}