3k^2-60k+57=0

Solution for 3k^2-60k+57=0 equation:

Simplifying
3k2 + -60k + 57 = 0

Reorder the terms:
57 + -60k + 3k2 = 0

Solving
57 + -60k + 3k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3'.
3(19 + -20k + k2) = 0

Factor a trinomial.
3((1 + -1k)(19 + -1k)) = 0

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

Simplifying
1 + -1k = 0

Solving
1 + -1k = 0

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

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

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

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

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

Simplifying
k = 1
Subproblem 2
Set the factor '(19 + -1k)' equal to zero and attempt to solve:

Simplifying
19 + -1k = 0

Solving
19 + -1k = 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 + -1k = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1k = 0 + -19
-1k = 0 + -19

Combine like terms: 0 + -19 = -19
-1k = -19

Divide each side by '-1'.
k = 19

Simplifying
k = 19
Solution
k = {1, 19}