32-12*k^2-k-32=0

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

Simplifying
32 + -12k2 + -1k + -32 = 0

Reorder the terms:
32 + -32 + -1k + -12k2 = 0

Combine like terms: 32 + -32 = 0
0 + -1k + -12k2 = 0
-1k + -12k2 = 0

Solving
-1k + -12k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '-1k'.
-1k(1 + 12k) = 0

Ignore the factor -1.
Subproblem 1
Set the factor 'k' equal to zero and attempt to solve:

Simplifying
k = 0

Solving
k = 0

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

Simplifying
k = 0
Subproblem 2
Set the factor '(1 + 12k)' equal to zero and attempt to solve:

Simplifying
1 + 12k = 0

Solving
1 + 12k = 0

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

Add '-1' to each side of the equation.
1 + -1 + 12k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 12k = 0 + -1
12k = 0 + -1

Combine like terms: 0 + -1 = -1
12k = -1

Divide each side by '12'.
k = -0.08333333333

Simplifying
k = -0.08333333333
Solution
k = {0, -0.08333333333}