=3k^2-33k+72

Solution for =3k^2-33k+72 equation:

Simplifying
0 = 3k2 + -33k + 72

Reorder the terms:
0 = 72 + -33k + 3k2

Solving
0 = 72 + -33k + 3k2

Solving for variable 'k'.

Combine like terms: 0 + -72 = -72
-72 + 33k + -3k2 = 72 + -33k + 3k2 + -72 + 33k + -3k2

Reorder the terms:
-72 + 33k + -3k2 = 72 + -72 + -33k + 33k + 3k2 + -3k2

Combine like terms: 72 + -72 = 0
-72 + 33k + -3k2 = 0 + -33k + 33k + 3k2 + -3k2
-72 + 33k + -3k2 = -33k + 33k + 3k2 + -3k2

Combine like terms: -33k + 33k = 0
-72 + 33k + -3k2 = 0 + 3k2 + -3k2
-72 + 33k + -3k2 = 3k2 + -3k2

Combine like terms: 3k2 + -3k2 = 0
-72 + 33k + -3k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + 11k + -1k2) = 0

Factor a trinomial.
3((-8 + k)(3 + -1k)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-8 + k)' equal to zero and attempt to solve:

Simplifying
-8 + k = 0

Solving
-8 + k = 0

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

Add '8' to each side of the equation.
-8 + 8 + k = 0 + 8

Combine like terms: -8 + 8 = 0
0 + k = 0 + 8
k = 0 + 8

Combine like terms: 0 + 8 = 8
k = 8

Simplifying
k = 8
Subproblem 2
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
Solution
k = {8, 3}