-12k^2+20k+57=0

Solution for -12k^2+20k+57=0 equation:

Simplifying
-12k2 + 20k + 57 = 0

Reorder the terms:
57 + 20k + -12k2 = 0

Solving
57 + 20k + -12k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(19 + -6k)(3 + 2k) = 0

Subproblem 1
Set the factor '(19 + -6k)' equal to zero and attempt to solve:

Simplifying
19 + -6k = 0

Solving
19 + -6k = 0

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

Add '-19' to each side of the equation.
19 + -19 + -6k = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -6k = 0 + -19
-6k = 0 + -19

Combine like terms: 0 + -19 = -19
-6k = -19

Divide each side by '-6'.
k = 3.166666667

Simplifying
k = 3.166666667
Subproblem 2
Set the factor '(3 + 2k)' equal to zero and attempt to solve:

Simplifying
3 + 2k = 0

Solving
3 + 2k = 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 + 2k = 0 + -3

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

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

Divide each side by '2'.
k = -1.5

Simplifying
k = -1.5
Solution
k = {3.166666667, -1.5}