6k^2-69=5k

Solution for 6k^2-69=5k equation:

Simplifying
6k2 + -69 = 5k

Reorder the terms:
-69 + 6k2 = 5k

Solving
-69 + 6k2 = 5k

Solving for variable 'k'.

Reorder the terms:
-69 + -5k + 6k2 = 5k + -5k

Combine like terms: 5k + -5k = 0
-69 + -5k + 6k2 = 0

Factor a trinomial.
(-3 + -1k)(23 + -6k) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(23 + -6k)' equal to zero and attempt to solve:

Simplifying
23 + -6k = 0

Solving
23 + -6k = 0

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

Add '-23' to each side of the equation.
23 + -23 + -6k = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -6k = 0 + -23
-6k = 0 + -23

Combine like terms: 0 + -23 = -23
-6k = -23

Divide each side by '-6'.
k = 3.833333333

Simplifying
k = 3.833333333
Solution
k = {-3, 3.833333333}