25uv^2(4u-v)+15u^2v(v-4u)=

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Solution for 25uv^2(4u-v)+15u^2v(v-4u)= equation: 


Simplifying
25uv2(4u + -1v) + 15u2v(v + -4u) = 0
(4u * 25uv2 + -1v * 25uv2) + 15u2v(v + -4u) = 0

Reorder the terms:
(-25uv3 + 100u2v2) + 15u2v(v + -4u) = 0
(-25uv3 + 100u2v2) + 15u2v(v + -4u) = 0

Reorder the terms:
-25uv3 + 100u2v2 + 15u2v(-4u + v) = 0
-25uv3 + 100u2v2 + (-4u * 15u2v + v * 15u2v) = 0

Reorder the terms:
-25uv3 + 100u2v2 + (15u2v2 + -60u3v) = 0
-25uv3 + 100u2v2 + (15u2v2 + -60u3v) = 0

Combine like terms: 100u2v2 + 15u2v2 = 115u2v2
-25uv3 + 115u2v2 + -60u3v = 0

Solving
-25uv3 + 115u2v2 + -60u3v = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '5uv'.
5uv(-5v2 + 23uv + -12u2) = 0

Factor a trinomial.
5uv((-5v + 3u)(v + -4u)) = 0

Ignore the factor 5.

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 + 3u)' equal to zero and attempt to solve:

Simplifying
-5v + 3u = 0

Reorder the terms:
3u + -5v = 0

Solving
3u + -5v = 0

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

Add '5v' to each side of the equation.
3u + -5v + 5v = 0 + 5v

Combine like terms: -5v + 5v = 0
3u + 0 = 0 + 5v
3u = 0 + 5v
Remove the zero:
3u = 5v

Divide each side by '3'.
u = 1.666666667v

Simplifying
u = 1.666666667v

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 = {1.666666667v, 0.25v}

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