7k^2+7k-210=0

Solution for 7k^2+7k-210=0 equation:

Simplifying
7k2 + 7k + -210 = 0

Reorder the terms:
-210 + 7k + 7k2 = 0

Solving
-210 + 7k + 7k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-30 + k + k2) = 0

Factor a trinomial.
7((-6 + -1k)(5 + -1k)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-6 + -1k)' equal to zero and attempt to solve:

Simplifying
-6 + -1k = 0

Solving
-6 + -1k = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1k = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1k = 0 + 6
-1k = 0 + 6

Combine like terms: 0 + 6 = 6
-1k = 6

Divide each side by '-1'.
k = -6

Simplifying
k = -6
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 = {-6, 5}