4k(4)+32k(3)+60k(2)=-4k(2)(k-3)(k-5)

Solution for 4k(4)+32k(3)+60k(2)=-4k(2)(k-3)(k-5) equation:

Simplifying
4k(4) + 32k(3) + 60k(2) = -4k(2)(k + -3)(k + -5)

Reorder the terms for easier multiplication:
4 * 4k + 32k(3) + 60k(2) = -4k(2)(k + -3)(k + -5)

Multiply 4 * 4
16k + 32k(3) + 60k(2) = -4k(2)(k + -3)(k + -5)

Reorder the terms for easier multiplication:
16k + 32 * 3k + 60k(2) = -4k(2)(k + -3)(k + -5)

Multiply 32 * 3
16k + 96k + 60k(2) = -4k(2)(k + -3)(k + -5)

Reorder the terms for easier multiplication:
16k + 96k + 60 * 2k = -4k(2)(k + -3)(k + -5)

Multiply 60 * 2
16k + 96k + 120k = -4k(2)(k + -3)(k + -5)

Combine like terms: 16k + 96k = 112k
112k + 120k = -4k(2)(k + -3)(k + -5)

Combine like terms: 112k + 120k = 232k
232k = -4k(2)(k + -3)(k + -5)

Reorder the terms:
232k = -4k * 2(-3 + k)(k + -5)

Reorder the terms:
232k = -4k * 2(-3 + k)(-5 + k)

Reorder the terms for easier multiplication:
232k = -4 * 2k(-3 + k)(-5 + k)

Multiply -4 * 2
232k = -8k(-3 + k)(-5 + k)

Multiply (-3 + k) * (-5 + k)
232k = -8k(-3(-5 + k) + k(-5 + k))
232k = -8k((-5 * -3 + k * -3) + k(-5 + k))
232k = -8k((15 + -3k) + k(-5 + k))
232k = -8k(15 + -3k + (-5 * k + k * k))
232k = -8k(15 + -3k + (-5k + k2))

Combine like terms: -3k + -5k = -8k
232k = -8k(15 + -8k + k2)
232k = (15 * -8k + -8k * -8k + k2 * -8k)
232k = (-120k + 64k2 + -8k3)

Solving
232k = -120k + 64k2 + -8k3

Solving for variable 'k'.

Combine like terms: 232k + 120k = 352k
352k + -64k2 + 8k3 = -120k + 64k2 + -8k3 + 120k + -64k2 + 8k3

Reorder the terms:
352k + -64k2 + 8k3 = -120k + 120k + 64k2 + -64k2 + -8k3 + 8k3

Combine like terms: -120k + 120k = 0
352k + -64k2 + 8k3 = 0 + 64k2 + -64k2 + -8k3 + 8k3
352k + -64k2 + 8k3 = 64k2 + -64k2 + -8k3 + 8k3

Combine like terms: 64k2 + -64k2 = 0
352k + -64k2 + 8k3 = 0 + -8k3 + 8k3
352k + -64k2 + 8k3 = -8k3 + 8k3

Combine like terms: -8k3 + 8k3 = 0
352k + -64k2 + 8k3 = 0

Factor out the Greatest Common Factor (GCF), '8k'.
8k(44 + -8k + k2) = 0

Ignore the factor 8.
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 '(44 + -8k + k2)' equal to zero and attempt to solve:

Simplifying
44 + -8k + k2 = 0

Solving
44 + -8k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-44' to each side of the equation.
44 + -8k + -44 + k2 = 0 + -44

Reorder the terms:
44 + -44 + -8k + k2 = 0 + -44

Combine like terms: 44 + -44 = 0
0 + -8k + k2 = 0 + -44
-8k + k2 = 0 + -44

Combine like terms: 0 + -44 = -44
-8k + k2 = -44

The k term is -8k.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8k + 16 + k2 = -44 + 16

Reorder the terms:
16 + -8k + k2 = -44 + 16

Combine like terms: -44 + 16 = -28
16 + -8k + k2 = -28

Factor a perfect square on the left side:
(k + -4)(k + -4) = -28

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
k = {0}