0=k^2+12k+32

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

Simplifying
0 = k2 + 12k + 32

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

Solving
0 = 32 + 12k + k2

Solving for variable 'k'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(32 + 12k + k2) = 0

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

Ignore the factor -1.
Subproblem 1
Set the factor '(8 + k)' equal to zero and attempt to solve:

Simplifying
8 + k = 0

Solving
8 + k = 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 + k = 0 + -8

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

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

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

Simplifying
4 + k = 0

Solving
4 + k = 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 + k = 0 + -4

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

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

Simplifying
k = -4
Solution
k = {-8, -4}