5k^2=-5+10k

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

Simplifying
5k2 = -5 + 10k

Solving
5k2 = -5 + 10k

Solving for variable 'k'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), '5'.
5(1 + -2k + k2) = 0

Factor a trinomial.
5((1 + -1k)(1 + -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 '(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
Solution
k = {1, 1}