9k^2+30k-24=0

Solution for 9k^2+30k-24=0 equation:

Simplifying
9k2 + 30k + -24 = 0

Reorder the terms:
-24 + 30k + 9k2 = 0

Solving
-24 + 30k + 9k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + 10k + 3k2) = 0

Factor a trinomial.
3((-4 + -1k)(2 + -3k)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -1k)' equal to zero and attempt to solve:

Simplifying
-4 + -1k = 0

Solving
-4 + -1k = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1k = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1k = 0 + 4
-1k = 0 + 4

Combine like terms: 0 + 4 = 4
-1k = 4

Divide each side by '-1'.
k = -4

Simplifying
k = -4
Subproblem 2
Set the factor '(2 + -3k)' equal to zero and attempt to solve:

Simplifying
2 + -3k = 0

Solving
2 + -3k = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3k = 0 + -2

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

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

Divide each side by '-3'.
k = 0.6666666667

Simplifying
k = 0.6666666667
Solution
k = {-4, 0.6666666667}