6k^2-13k=5

Solution for 6k^2-13k=5 equation:

Simplifying
6k2 + -13k = 5

Reorder the terms:
-13k + 6k2 = 5

Solving
-13k + 6k2 = 5

Solving for variable 'k'.

Reorder the terms:
-5 + -13k + 6k2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -13k + 6k2 = 0

Factor a trinomial.
(-1 + -3k)(5 + -2k) = 0

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

Simplifying
-1 + -3k = 0

Solving
-1 + -3k = 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 + -3k = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3k = 0 + 1
-3k = 0 + 1

Combine like terms: 0 + 1 = 1
-3k = 1

Divide each side by '-3'.
k = -0.3333333333

Simplifying
k = -0.3333333333
Subproblem 2
Set the factor '(5 + -2k)' equal to zero and attempt to solve:

Simplifying
5 + -2k = 0

Solving
5 + -2k = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2k = 0 + -5
-2k = 0 + -5

Combine like terms: 0 + -5 = -5
-2k = -5

Divide each side by '-2'.
k = 2.5

Simplifying
k = 2.5
Solution
k = {-0.3333333333, 2.5}