0=-2k^2+12k-10

Solution for 0=-2k^2+12k-10 equation:

Simplifying
0 = -2k2 + 12k + -10

Reorder the terms:
0 = -10 + 12k + -2k2

Solving
0 = -10 + 12k + -2k2

Solving for variable 'k'.

Combine like terms: 0 + 10 = 10
10 + -12k + 2k2 = -10 + 12k + -2k2 + 10 + -12k + 2k2

Reorder the terms:
10 + -12k + 2k2 = -10 + 10 + 12k + -12k + -2k2 + 2k2

Combine like terms: -10 + 10 = 0
10 + -12k + 2k2 = 0 + 12k + -12k + -2k2 + 2k2
10 + -12k + 2k2 = 12k + -12k + -2k2 + 2k2

Combine like terms: 12k + -12k = 0
10 + -12k + 2k2 = 0 + -2k2 + 2k2
10 + -12k + 2k2 = -2k2 + 2k2

Combine like terms: -2k2 + 2k2 = 0
10 + -12k + 2k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -6k + 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}