-4k^2+2k+30=0

Solution for -4k^2+2k+30=0 equation:

Simplifying
-4k2 + 2k + 30 = 0

Reorder the terms:
30 + 2k + -4k2 = 0

Solving
30 + 2k + -4k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + k + -2k2) = 0

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

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

Simplifying
3 + -1k = 0

Solving
3 + -1k = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1k = 0 + -3
-1k = 0 + -3

Combine like terms: 0 + -3 = -3
-1k = -3

Divide each side by '-1'.
k = 3

Simplifying
k = 3
Subproblem 2
Set the factor '(5 + 2k)' equal to zero and attempt to solve:

Simplifying
5 + 2k = 0

Solving
5 + 2k = 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 + 2k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2k = 0 + -5
2k = 0 + -5

Combine like terms: 0 + -5 = -5
2k = -5

Divide each side by '2'.
k = -2.5

Simplifying
k = -2.5
Solution
k = {3, -2.5}