m^2=5m-6

Solution for m^2=5m-6 equation:

Simplifying
m2 = 5m + -6

Reorder the terms:
m2 = -6 + 5m

Solving
m2 = -6 + 5m

Solving for variable 'm'.

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

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

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

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

Factor a trinomial.
(2 + -1m)(3 + -1m) = 0

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

Simplifying
2 + -1m = 0

Solving
2 + -1m = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1m = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1m = 0 + -2
-1m = 0 + -2

Combine like terms: 0 + -2 = -2
-1m = -2

Divide each side by '-1'.
m = 2

Simplifying
m = 2
Subproblem 2
Set the factor '(3 + -1m)' equal to zero and attempt to solve:

Simplifying
3 + -1m = 0

Solving
3 + -1m = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1m = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1m = 0 + -3
-1m = 0 + -3

Combine like terms: 0 + -3 = -3
-1m = -3

Divide each side by '-1'.
m = 3

Simplifying
m = 3
Solution
m = {2, 3}