20uv^2(4u-v)+8u^2v(v-4u)=

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Solution for 20uv^2(4u-v)+8u^2v(v-4u)= equation: 


Simplifying
20uv2(4u + -1v) + 8u2v(v + -4u) = 0
(4u * 20uv2 + -1v * 20uv2) + 8u2v(v + -4u) = 0

Reorder the terms:
(-20uv3 + 80u2v2) + 8u2v(v + -4u) = 0
(-20uv3 + 80u2v2) + 8u2v(v + -4u) = 0

Reorder the terms:
-20uv3 + 80u2v2 + 8u2v(-4u + v) = 0
-20uv3 + 80u2v2 + (-4u * 8u2v + v * 8u2v) = 0

Reorder the terms:
-20uv3 + 80u2v2 + (8u2v2 + -32u3v) = 0
-20uv3 + 80u2v2 + (8u2v2 + -32u3v) = 0

Combine like terms: 80u2v2 + 8u2v2 = 88u2v2
-20uv3 + 88u2v2 + -32u3v = 0

Solving
-20uv3 + 88u2v2 + -32u3v = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '4uv'.
4uv(-5v2 + 22uv + -8u2) = 0

Factor a trinomial.
4uv((-5v + 2u)(v + -4u)) = 0

Ignore the factor 4.

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

Simplifying
uv = 0

Solving
uv = 0

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

Simplifying
uv = 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 '(-5v + 2u)' equal to zero and attempt to solve:

Simplifying
-5v + 2u = 0

Reorder the terms:
2u + -5v = 0

Solving
2u + -5v = 0

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

Add '5v' to each side of the equation.
2u + -5v + 5v = 0 + 5v

Combine like terms: -5v + 5v = 0
2u + 0 = 0 + 5v
2u = 0 + 5v
Remove the zero:
2u = 5v

Divide each side by '2'.
u = 2.5v

Simplifying
u = 2.5v

Subproblem 3
Set the factor '(v + -4u)' equal to zero and attempt to solve:

Simplifying
v + -4u = 0

Reorder the terms:
-4u + v = 0

Solving
-4u + v = 0

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

Add '-1v' to each side of the equation.
-4u + v + -1v = 0 + -1v

Combine like terms: v + -1v = 0
-4u + 0 = 0 + -1v
-4u = 0 + -1v
Remove the zero:
-4u = -1v

Divide each side by '-4'.
u = 0.25v

Simplifying
u = 0.25v
Solution
u = {2.5v, 0.25v}

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