5k^2=6-k

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

Simplifying
5k2 = 6 + -1k

Solving
5k2 = 6 + -1k

Solving for variable 'k'.

Reorder the terms:
-6 + k + 5k2 = 6 + -1k + -6 + k

Reorder the terms:
-6 + k + 5k2 = 6 + -6 + -1k + k

Combine like terms: 6 + -6 = 0
-6 + k + 5k2 = 0 + -1k + k
-6 + k + 5k2 = -1k + k

Combine like terms: -1k + k = 0
-6 + k + 5k2 = 0

Factor a trinomial.
(-6 + -5k)(1 + -1k) = 0

Subproblem 1
Set the factor '(-6 + -5k)' equal to zero and attempt to solve:

Simplifying
-6 + -5k = 0

Solving
-6 + -5k = 0

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

Add '6' to each side of the equation.
-6 + 6 + -5k = 0 + 6

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

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

Divide each side by '-5'.
k = -1.2

Simplifying
k = -1.2
Subproblem 2
Set the factor '(1 + -1k)' equal to zero and attempt to solve:

Simplifying
1 + -1k = 0

Solving
1 + -1k = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1k = 0 + -1
-1k = 0 + -1

Combine like terms: 0 + -1 = -1
-1k = -1

Divide each side by '-1'.
k = 1

Simplifying
k = 1
Solution
k = {-1.2, 1}