6k^2-42k+72=0

Solution for 6k^2-42k+72=0 equation:

Simplifying
6k2 + -42k + 72 = 0

Reorder the terms:
72 + -42k + 6k2 = 0

Solving
72 + -42k + 6k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '6'.
6(12 + -7k + k2) = 0

Factor a trinomial.
6((3 + -1k)(4 + -1k)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(3 + -1k)' equal to zero and attempt to solve:

Simplifying
3 + -1k = 0

Solving
3 + -1k = 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 + -1k = 0 + -3

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

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

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

Simplifying
k = 3
Subproblem 2
Set the factor '(4 + -1k)' equal to zero and attempt to solve:

Simplifying
4 + -1k = 0

Solving
4 + -1k = 0

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

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

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

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

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

Simplifying
k = 4
Solution
k = {3, 4}