3k^2-2k=21

Solution for 3k^2-2k=21 equation:

Simplifying
3k2 + -2k = 21

Reorder the terms:
-2k + 3k2 = 21

Solving
-2k + 3k2 = 21

Solving for variable 'k'.

Reorder the terms:
-21 + -2k + 3k2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + -2k + 3k2 = 0

Factor a trinomial.
(-7 + -3k)(3 + -1k) = 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 + -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 = {-2.333333333, 3}