4km^2(8km^2+2k^2m+5k)=0

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Solution for 4km^2(8km^2+2k^2m+5k)=0 equation: 


Simplifying
4km2(8km2 + 2k2m + 5k) = 0

Reorder the terms:
4km2(5k + 8km2 + 2k2m) = 0
(5k * 4km2 + 8km2 * 4km2 + 2k2m * 4km2) = 0
(20k2m2 + 32k2m4 + 8k3m3) = 0

Solving
20k2m2 + 32k2m4 + 8k3m3 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '4k2m2'.
4k2m2(5 + 8m2 + 2km) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'k2m2' equal to zero and attempt to solve:

Simplifying
k2m2 = 0

Solving
k2m2 = 0

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

Simplifying
k2m2 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(5 + 8m2 + 2km)' equal to zero and attempt to solve:

Simplifying
5 + 8m2 + 2km = 0

Reorder the terms:
5 + 2km + 8m2 = 0

Solving
5 + 2km + 8m2 = 0

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

Add '-5' to each side of the equation.
5 + 2km + -5 + 8m2 = 0 + -5

Reorder the terms:
5 + -5 + 2km + 8m2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2km + 8m2 = 0 + -5
2km + 8m2 = 0 + -5

Combine like terms: 0 + -5 = -5
2km + 8m2 = -5

Add '-8m2' to each side of the equation.
2km + 8m2 + -8m2 = -5 + -8m2

Combine like terms: 8m2 + -8m2 = 0
2km + 0 = -5 + -8m2
2km = -5 + -8m2

Divide each side by '2m'.
k = -2.5m-1 + -4m

Simplifying
k = -2.5m-1 + -4m
Solution
k = {-2.5m-1 + -4m}

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