12k^2-84k+99=0

Solution for 12k^2-84k+99=0 equation:

Simplifying
12k2 + -84k + 99 = 0

Reorder the terms:
99 + -84k + 12k2 = 0

Solving
99 + -84k + 12k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3'.
3(33 + -28k + 4k2) = 0

Factor a trinomial.
3((3 + -2k)(11 + -2k)) = 0

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

Simplifying
3 + -2k = 0

Solving
3 + -2k = 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 + -2k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2k = 0 + -3
-2k = 0 + -3

Combine like terms: 0 + -3 = -3
-2k = -3

Divide each side by '-2'.
k = 1.5

Simplifying
k = 1.5
Subproblem 2
Set the factor '(11 + -2k)' equal to zero and attempt to solve:

Simplifying
11 + -2k = 0

Solving
11 + -2k = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2k = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2k = 0 + -11
-2k = 0 + -11

Combine like terms: 0 + -11 = -11
-2k = -11

Divide each side by '-2'.
k = 5.5

Simplifying
k = 5.5
Solution
k = {1.5, 5.5}