10(w^6)-160(w^2)(v^4)=0

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Solution for 10(w^6)-160(w^2)(v^4)=0 equation: 


Simplifying
10(w6) + -160(w2)(v4) = 0

Multiply w2 * v4
10w6 + -160v4w2 = 0

Reorder the terms:
-160v4w2 + 10w6 = 0

Solving
-160v4w2 + 10w6 = 0

Solving for variable 'v'.

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

Add '-10w6' to each side of the equation.
-160v4w2 + 10w6 + -10w6 = 0 + -10w6

Combine like terms: 10w6 + -10w6 = 0
-160v4w2 + 0 = 0 + -10w6
-160v4w2 = 0 + -10w6
Remove the zero:
-160v4w2 = -10w6

Divide each side by '-160w2'.
v4 = 0.0625w4

Simplifying
v4 = 0.0625w4

Combine like terms: 0.0625w4 + -0.0625w4 = 0.0000
v4 + -0.0625w4 = 0.0000

Factor a difference between two squares.
(v2 + 0.25w2)(v2 + -0.25w2) = 0.0000

Factor a difference between two squares.
(v2 + 0.25w2)((v + 0.5w)(v + -0.5w)) = 0.0000


Subproblem 1
Set the factor '(v2 + 0.25w2)' equal to zero and attempt to solve:

Simplifying
v2 + 0.25w2 = 0

Solving
v2 + 0.25w2 = 0

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

Add '-0.25w2' to each side of the equation.
v2 + 0.25w2 + -0.25w2 = 0 + -0.25w2

Combine like terms: 0.25w2 + -0.25w2 = 0.00
v2 + 0.00 = 0 + -0.25w2
v2 = 0 + -0.25w2
Remove the zero:
v2 = -0.25w2

Simplifying
v2 = -0.25w2

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 '(v + 0.5w)' equal to zero and attempt to solve:

Simplifying
v + 0.5w = 0

Solving
v + 0.5w = 0

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

Add '-0.5w' to each side of the equation.
v + 0.5w + -0.5w = 0 + -0.5w

Combine like terms: 0.5w + -0.5w = 0.0
v + 0.0 = 0 + -0.5w
v = 0 + -0.5w
Remove the zero:
v = -0.5w

Simplifying
v = -0.5w

Subproblem 3
Set the factor '(v + -0.5w)' equal to zero and attempt to solve:

Simplifying
v + -0.5w = 0

Solving
v + -0.5w = 0

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

Add '0.5w' to each side of the equation.
v + -0.5w + 0.5w = 0 + 0.5w

Combine like terms: -0.5w + 0.5w = 0.0
v + 0.0 = 0 + 0.5w
v = 0 + 0.5w
Remove the zero:
v = 0.5w

Simplifying
v = 0.5w
Solution
v = {-0.5w, 0.5w}

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