4k^2+60-32k=0

Solution for 4k^2+60-32k=0 equation:

Simplifying
4k2 + 60 + -32k = 0

Reorder the terms:
60 + -32k + 4k2 = 0

Solving
60 + -32k + 4k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '4'.
4(15 + -8k + k2) = 0

Factor a trinomial.
4((3 + -1k)(5 + -1k)) = 0

Ignore the factor 4.
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 + -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 = {3, 5}