4k^2+4k-24=0

Solution for 4k^2+4k-24=0 equation:

Simplifying
4k2 + 4k + -24 = 0

Reorder the terms:
-24 + 4k + 4k2 = 0

Solving
-24 + 4k + 4k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + k + k2) = 0

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

Ignore the factor 4.
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 '(2 + -1k)' equal to zero and attempt to solve:

Simplifying
2 + -1k = 0

Solving
2 + -1k = 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 + -1k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1k = 0 + -2
-1k = 0 + -2

Combine like terms: 0 + -2 = -2
-1k = -2

Divide each side by '-1'.
k = 2

Simplifying
k = 2
Solution
k = {-3, 2}