2k^2-8k=10

Solution for 2k^2-8k=10 equation:

Simplifying
2k2 + -8k = 10

Reorder the terms:
-8k + 2k2 = 10

Solving
-8k + 2k2 = 10

Solving for variable 'k'.

Reorder the terms:
-10 + -8k + 2k2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -8k + 2k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -4k + k2) = 0

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(5 + -1k)' equal to zero and attempt to solve:

Simplifying
5 + -1k = 0

Solving
5 + -1k = 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 + -1k = 0 + -5

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

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

Divide each side by '-1'.
k = 5

Simplifying
k = 5
Solution
k = {-1, 5}