3k^2+72=33k

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

Simplifying
3k2 + 72 = 33k

Reorder the terms:
72 + 3k2 = 33k

Solving
72 + 3k2 = 33k

Solving for variable 'k'.

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

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

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

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

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

Simplifying
8 + -1k = 0

Solving
8 + -1k = 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 + -1k = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1k = 0 + -8
-1k = 0 + -8

Combine like terms: 0 + -8 = -8
-1k = -8

Divide each side by '-1'.
k = 8

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