3k^2-9k=54

Solution for 3k^2-9k=54 equation:

Simplifying
3k2 + -9k = 54

Reorder the terms:
-9k + 3k2 = 54

Solving
-9k + 3k2 = 54

Solving for variable 'k'.

Reorder the terms:
-54 + -9k + 3k2 = 54 + -54

Combine like terms: 54 + -54 = 0
-54 + -9k + 3k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-18 + -3k + k2) = 0

Factor a trinomial.
3((-3 + -1k)(6 + -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 '(6 + -1k)' equal to zero and attempt to solve:

Simplifying
6 + -1k = 0

Solving
6 + -1k = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1k = 0 + -6

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

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

Divide each side by '-1'.
k = 6

Simplifying
k = 6
Solution
k = {-3, 6}