6k^2-100=-10k

Solution for 6k^2-100=-10k equation:

Simplifying
6k2 + -100 = -10k

Reorder the terms:
-100 + 6k2 = -10k

Solving
-100 + 6k2 = -10k

Solving for variable 'k'.

Reorder the terms:
-100 + 10k + 6k2 = -10k + 10k

Combine like terms: -10k + 10k = 0
-100 + 10k + 6k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + 5k + 3k2) = 0

Factor a trinomial.
2((-5 + -1k)(10 + -3k)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(10 + -3k)' equal to zero and attempt to solve:

Simplifying
10 + -3k = 0

Solving
10 + -3k = 0

Move all terms containing k to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + -3k = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3k = 0 + -10
-3k = 0 + -10

Combine like terms: 0 + -10 = -10
-3k = -10

Divide each side by '-3'.
k = 3.333333333

Simplifying
k = 3.333333333
Solution
k = {-5, 3.333333333}