10uv^2(3u-v)+12u^2v(v-3u)=

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Solution for 10uv^2(3u-v)+12u^2v(v-3u)= equation: 


Simplifying
10uv2(3u + -1v) + 12u2v(v + -3u) = 0
(3u * 10uv2 + -1v * 10uv2) + 12u2v(v + -3u) = 0

Reorder the terms:
(-10uv3 + 30u2v2) + 12u2v(v + -3u) = 0
(-10uv3 + 30u2v2) + 12u2v(v + -3u) = 0

Reorder the terms:
-10uv3 + 30u2v2 + 12u2v(-3u + v) = 0
-10uv3 + 30u2v2 + (-3u * 12u2v + v * 12u2v) = 0

Reorder the terms:
-10uv3 + 30u2v2 + (12u2v2 + -36u3v) = 0
-10uv3 + 30u2v2 + (12u2v2 + -36u3v) = 0

Combine like terms: 30u2v2 + 12u2v2 = 42u2v2
-10uv3 + 42u2v2 + -36u3v = 0

Solving
-10uv3 + 42u2v2 + -36u3v = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2uv'.
2uv(-5v2 + 21uv + -18u2) = 0

Factor a trinomial.
2uv((-5v + 6u)(v + -3u)) = 0

Ignore the factor 2.

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 + 6u)' equal to zero and attempt to solve:

Simplifying
-5v + 6u = 0

Reorder the terms:
6u + -5v = 0

Solving
6u + -5v = 0

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

Add '5v' to each side of the equation.
6u + -5v + 5v = 0 + 5v

Combine like terms: -5v + 5v = 0
6u + 0 = 0 + 5v
6u = 0 + 5v
Remove the zero:
6u = 5v

Divide each side by '6'.
u = 0.8333333333v

Simplifying
u = 0.8333333333v

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

Simplifying
v + -3u = 0

Reorder the terms:
-3u + v = 0

Solving
-3u + v = 0

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

Add '-1v' to each side of the equation.
-3u + v + -1v = 0 + -1v

Combine like terms: v + -1v = 0
-3u + 0 = 0 + -1v
-3u = 0 + -1v
Remove the zero:
-3u = -1v

Divide each side by '-3'.
u = 0.3333333333v

Simplifying
u = 0.3333333333v
Solution
u = {0.8333333333v, 0.3333333333v}

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