3k^2-11k=-6

Solution for 3k^2-11k=-6 equation:

Simplifying
3k2 + -11k = -6

Reorder the terms:
-11k + 3k2 = -6

Solving
-11k + 3k2 = -6

Solving for variable 'k'.

Reorder the terms:
6 + -11k + 3k2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + -11k + 3k2 = 0

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

Subproblem 1
Set the factor '(2 + -3k)' equal to zero and attempt to solve:

Simplifying
2 + -3k = 0

Solving
2 + -3k = 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 + -3k = 0 + -2

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

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

Divide each side by '-3'.
k = 0.6666666667

Simplifying
k = 0.6666666667
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 = {0.6666666667, 3}