5k^2-25k+30=0

Solution for 5k^2-25k+30=0 equation:

Simplifying
5k2 + -25k + 30 = 0

Reorder the terms:
30 + -25k + 5k2 = 0

Solving
30 + -25k + 5k2 = 0

Solving for variable 'k'.

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

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

Ignore the factor 5.
Subproblem 1
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
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 = {2, 3}