6u^4-120u^3v+600u^2v^2=0

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Solution for 6u^4-120u^3v+600u^2v^2=0 equation: 


Simplifying
6u4 + -120u3v + 600u2v2 = 0

Reorder the terms:
600u2v2 + -120u3v + 6u4 = 0

Solving
600u2v2 + -120u3v + 6u4 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '6u2'.
6u2(100v2 + -20uv + u2) = 0

Factor a trinomial.
6u2((10v + -1u)(10v + -1u)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor 'u2' equal to zero and attempt to solve:

Simplifying
u2 = 0

Solving
u2 = 0

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

Simplifying
u2 = 0

Take the square root of each side:
u = {0}

Subproblem 2
Set the factor '(10v + -1u)' equal to zero and attempt to solve:

Simplifying
10v + -1u = 0

Reorder the terms:
-1u + 10v = 0

Solving
-1u + 10v = 0

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

Add '-10v' to each side of the equation.
-1u + 10v + -10v = 0 + -10v

Combine like terms: 10v + -10v = 0
-1u + 0 = 0 + -10v
-1u = 0 + -10v
Remove the zero:
-1u = -10v

Divide each side by '-1'.
u = 10v

Simplifying
u = 10v

Subproblem 3
Set the factor '(10v + -1u)' equal to zero and attempt to solve:

Simplifying
10v + -1u = 0

Reorder the terms:
-1u + 10v = 0

Solving
-1u + 10v = 0

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

Add '-10v' to each side of the equation.
-1u + 10v + -10v = 0 + -10v

Combine like terms: 10v + -10v = 0
-1u + 0 = 0 + -10v
-1u = 0 + -10v
Remove the zero:
-1u = -10v

Divide each side by '-1'.
u = 10v

Simplifying
u = 10v
Solution
u = {0, 10v, 10v}

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