5k^2+12k-32=0

Solution for 5k^2+12k-32=0 equation:

Simplifying
5k2 + 12k + -32 = 0

Reorder the terms:
-32 + 12k + 5k2 = 0

Solving
-32 + 12k + 5k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-4 + -1k)(8 + -5k) = 0

Subproblem 1
Set the factor '(-4 + -1k)' equal to zero and attempt to solve:

Simplifying
-4 + -1k = 0

Solving
-4 + -1k = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1k = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1k = 0 + 4
-1k = 0 + 4

Combine like terms: 0 + 4 = 4
-1k = 4

Divide each side by '-1'.
k = -4

Simplifying
k = -4
Subproblem 2
Set the factor '(8 + -5k)' equal to zero and attempt to solve:

Simplifying
8 + -5k = 0

Solving
8 + -5k = 0

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

Add '-8' to each side of the equation.
8 + -8 + -5k = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5k = 0 + -8
-5k = 0 + -8

Combine like terms: 0 + -8 = -8
-5k = -8

Divide each side by '-5'.
k = 1.6

Simplifying
k = 1.6
Solution
k = {-4, 1.6}