105k^2-98k+21=0

Solution for 105k^2-98k+21=0 equation:

Simplifying
105k2 + -98k + 21 = 0

Reorder the terms:
21 + -98k + 105k2 = 0

Solving
21 + -98k + 105k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '7'.
7(3 + -14k + 15k2) = 0

Factor a trinomial.
7((1 + -3k)(3 + -5k)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(1 + -3k)' equal to zero and attempt to solve:

Simplifying
1 + -3k = 0

Solving
1 + -3k = 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 + -3k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3k = 0 + -1
-3k = 0 + -1

Combine like terms: 0 + -1 = -1
-3k = -1

Divide each side by '-3'.
k = 0.3333333333

Simplifying
k = 0.3333333333
Subproblem 2
Set the factor '(3 + -5k)' equal to zero and attempt to solve:

Simplifying
3 + -5k = 0

Solving
3 + -5k = 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 + -5k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5k = 0 + -3
-5k = 0 + -3

Combine like terms: 0 + -3 = -3
-5k = -3

Divide each side by '-5'.
k = 0.6

Simplifying
k = 0.6
Solution
k = {0.3333333333, 0.6}