21k^2+119k-42=0

Solution for 21k^2+119k-42=0 equation:

Simplifying
21k2 + 119k + -42 = 0

Reorder the terms:
-42 + 119k + 21k2 = 0

Solving
-42 + 119k + 21k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-6 + 17k + 3k2) = 0

Factor a trinomial.
7((-6 + -1k)(1 + -3k)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-6 + -1k)' equal to zero and attempt to solve:

Simplifying
-6 + -1k = 0

Solving
-6 + -1k = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1k = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1k = 0 + 6
-1k = 0 + 6

Combine like terms: 0 + 6 = 6
-1k = 6

Divide each side by '-1'.
k = -6

Simplifying
k = -6
Subproblem 2
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
Solution
k = {-6, 0.3333333333}