5k^2-15k=-10

Solution for 5k^2-15k=-10 equation:

Simplifying
5k2 + -15k = -10

Reorder the terms:
-15k + 5k2 = -10

Solving
-15k + 5k2 = -10

Solving for variable 'k'.

Reorder the terms:
10 + -15k + 5k2 = -10 + 10

Combine like terms: -10 + 10 = 0
10 + -15k + 5k2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + -3k + k2) = 0

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

Ignore the factor 5.
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 '(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
Solution
k = {1, 2}