4k^2+48k=-128

Solution for 4k^2+48k=-128 equation:

Simplifying
4k2 + 48k = -128

Reorder the terms:
48k + 4k2 = -128

Solving
48k + 4k2 = -128

Solving for variable 'k'.

Reorder the terms:
128 + 48k + 4k2 = -128 + 128

Combine like terms: -128 + 128 = 0
128 + 48k + 4k2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(32 + 12k + k2) = 0

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

Ignore the factor 4.
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}