0=k^2-5k+6

Solution for 0=k^2-5k+6 equation:

Simplifying
0 = k2 + -5k + 6

Reorder the terms:
0 = 6 + -5k + k2

Solving
0 = 6 + -5k + k2

Solving for variable 'k'.

Combine like terms: 0 + -6 = -6
-6 + 5k + -1k2 = 6 + -5k + k2 + -6 + 5k + -1k2

Reorder the terms:
-6 + 5k + -1k2 = 6 + -6 + -5k + 5k + k2 + -1k2

Combine like terms: 6 + -6 = 0
-6 + 5k + -1k2 = 0 + -5k + 5k + k2 + -1k2
-6 + 5k + -1k2 = -5k + 5k + k2 + -1k2

Combine like terms: -5k + 5k = 0
-6 + 5k + -1k2 = 0 + k2 + -1k2
-6 + 5k + -1k2 = k2 + -1k2

Combine like terms: k2 + -1k2 = 0
-6 + 5k + -1k2 = 0

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

Subproblem 1
Set the factor '(-3 + k)' equal to zero and attempt to solve:

Simplifying
-3 + k = 0

Solving
-3 + k = 0

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

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

Combine like terms: -3 + 3 = 0
0 + k = 0 + 3
k = 0 + 3

Combine like terms: 0 + 3 = 3
k = 3

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

Simplifying
2 + -1k = 0

Solving
2 + -1k = 0

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

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

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

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

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

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