20k^2-52k=24

Solution for 20k^2-52k=24 equation:

Simplifying
20k2 + -52k = 24

Reorder the terms:
-52k + 20k2 = 24

Solving
-52k + 20k2 = 24

Solving for variable 'k'.

Reorder the terms:
-24 + -52k + 20k2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + -52k + 20k2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + -13k + 5k2) = 0

Factor a trinomial.
4((-2 + -5k)(3 + -1k)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-2 + -5k)' equal to zero and attempt to solve:

Simplifying
-2 + -5k = 0

Solving
-2 + -5k = 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 + -5k = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5k = 0 + 2
-5k = 0 + 2

Combine like terms: 0 + 2 = 2
-5k = 2

Divide each side by '-5'.
k = -0.4

Simplifying
k = -0.4
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 = {-0.4, 3}