15k^2+12k-41=-5

Solution for 15k^2+12k-41=-5 equation:

Simplifying
15k2 + 12k + -41 = -5

Reorder the terms:
-41 + 12k + 15k2 = -5

Solving
-41 + 12k + 15k2 = -5

Solving for variable 'k'.

Reorder the terms:
-41 + 5 + 12k + 15k2 = -5 + 5

Combine like terms: -41 + 5 = -36
-36 + 12k + 15k2 = -5 + 5

Combine like terms: -5 + 5 = 0
-36 + 12k + 15k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + 4k + 5k2) = 0

Factor a trinomial.
3((-2 + -1k)(6 + -5k)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(6 + -5k)' equal to zero and attempt to solve:

Simplifying
6 + -5k = 0

Solving
6 + -5k = 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 + -5k = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5k = 0 + -6
-5k = 0 + -6

Combine like terms: 0 + -6 = -6
-5k = -6

Divide each side by '-5'.
k = 1.2

Simplifying
k = 1.2
Solution
k = {-2, 1.2}