9k^2-12k-51=-6

Solution for 9k^2-12k-51=-6 equation:

Simplifying
9k2 + -12k + -51 = -6

Reorder the terms:
-51 + -12k + 9k2 = -6

Solving
-51 + -12k + 9k2 = -6

Solving for variable 'k'.

Reorder the terms:
-51 + 6 + -12k + 9k2 = -6 + 6

Combine like terms: -51 + 6 = -45
-45 + -12k + 9k2 = -6 + 6

Combine like terms: -6 + 6 = 0
-45 + -12k + 9k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -4k + 3k2) = 0

Factor a trinomial.
3((-5 + -3k)(3 + -1k)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -3k)' equal to zero and attempt to solve:

Simplifying
-5 + -3k = 0

Solving
-5 + -3k = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3k = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3k = 0 + 5
-3k = 0 + 5

Combine like terms: 0 + 5 = 5
-3k = 5

Divide each side by '-3'.
k = -1.666666667

Simplifying
k = -1.666666667
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 = {-1.666666667, 3}