2k^2-k=10

Solution for 2k^2-k=10 equation:

Simplifying
2k2 + -1k = 10

Reorder the terms:
-1k + 2k2 = 10

Solving
-1k + 2k2 = 10

Solving for variable 'k'.

Reorder the terms:
-10 + -1k + 2k2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -1k + 2k2 = 0

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

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

Simplifying
-2 + -1k = 0

Solving
-2 + -1k = 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 + -1k = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1k = 0 + 2
-1k = 0 + 2

Combine like terms: 0 + 2 = 2
-1k = 2

Divide each side by '-1'.
k = -2

Simplifying
k = -2
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 = {-2, 2.5}