6k^2+5k-21=0

Solution for 6k^2+5k-21=0 equation:

Simplifying
6k2 + 5k + -21 = 0

Reorder the terms:
-21 + 5k + 6k2 = 0

Solving
-21 + 5k + 6k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-7 + -3k)(3 + -2k) = 0

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

Simplifying
-7 + -3k = 0

Solving
-7 + -3k = 0

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

Add '7' to each side of the equation.
-7 + 7 + -3k = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3k = 0 + 7
-3k = 0 + 7

Combine like terms: 0 + 7 = 7
-3k = 7

Divide each side by '-3'.
k = -2.333333333

Simplifying
k = -2.333333333
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 = {-2.333333333, 1.5}