m=m^2-5m+6

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

Simplifying
m = m2 + -5m + 6

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

Solving
m = 6 + -5m + m2

Solving for variable 'm'.

Reorder the terms:
-6 + m + 5m + -1m2 = 6 + -5m + m2 + -6 + 5m + -1m2

Combine like terms: m + 5m = 6m
-6 + 6m + -1m2 = 6 + -5m + m2 + -6 + 5m + -1m2

Reorder the terms:
-6 + 6m + -1m2 = 6 + -6 + -5m + 5m + m2 + -1m2

Combine like terms: 6 + -6 = 0
-6 + 6m + -1m2 = 0 + -5m + 5m + m2 + -1m2
-6 + 6m + -1m2 = -5m + 5m + m2 + -1m2

Combine like terms: -5m + 5m = 0
-6 + 6m + -1m2 = 0 + m2 + -1m2
-6 + 6m + -1m2 = m2 + -1m2

Combine like terms: m2 + -1m2 = 0
-6 + 6m + -1m2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
6 + -6m + m2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -6m + -6 + m2 = 0 + -6

Reorder the terms:
6 + -6 + -6m + m2 = 0 + -6

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

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

The m term is -6m.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6m + 9 + m2 = -6 + 9

Reorder the terms:
9 + -6m + m2 = -6 + 9

Combine like terms: -6 + 9 = 3
9 + -6m + m2 = 3

Factor a perfect square on the left side:
(m + -3)(m + -3) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(m + -3) equal to 1.732050808 and -1.732050808.

Subproblem 1
m + -3 = 1.732050808

Simplifying
m + -3 = 1.732050808

Reorder the terms:
-3 + m = 1.732050808

Solving
-3 + m = 1.732050808

Solving for variable 'm'.

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

Add '3' to each side of the equation.
-3 + 3 + m = 1.732050808 + 3

Combine like terms: -3 + 3 = 0
0 + m = 1.732050808 + 3
m = 1.732050808 + 3

Combine like terms: 1.732050808 + 3 = 4.732050808
m = 4.732050808

Simplifying
m = 4.732050808

Subproblem 2
m + -3 = -1.732050808

Simplifying
m + -3 = -1.732050808

Reorder the terms:
-3 + m = -1.732050808

Solving
-3 + m = -1.732050808

Solving for variable 'm'.

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

Add '3' to each side of the equation.
-3 + 3 + m = -1.732050808 + 3

Combine like terms: -3 + 3 = 0
0 + m = -1.732050808 + 3
m = -1.732050808 + 3

Combine like terms: -1.732050808 + 3 = 1.267949192
m = 1.267949192

Simplifying
m = 1.267949192

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {4.732050808, 1.267949192}