4k^2-24k=-36

Solution for 4k^2-24k=-36 equation:

Simplifying
4k2 + -24k = -36

Reorder the terms:
-24k + 4k2 = -36

Solving
-24k + 4k2 = -36

Solving for variable 'k'.

Reorder the terms:
36 + -24k + 4k2 = -36 + 36

Combine like terms: -36 + 36 = 0
36 + -24k + 4k2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(9 + -6k + k2) = 0

Factor a trinomial.
4((3 + -1k)(3 + -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 '(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 = {3, 3}