6k^2=5k+6

Solution for 6k^2=5k+6 equation:

Simplifying
6k2 = 5k + 6

Reorder the terms:
6k2 = 6 + 5k

Solving
6k2 = 6 + 5k

Solving for variable 'k'.

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

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

Combine like terms: 6 + -6 = 0
-6 + -5k + 6k2 = 0 + 5k + -5k
-6 + -5k + 6k2 = 5k + -5k

Combine like terms: 5k + -5k = 0
-6 + -5k + 6k2 = 0

Factor a trinomial.
(-2 + -3k)(3 + -2k) = 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 + -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 = {-0.6666666667, 1.5}