(8v+ux^2)(v-ux^2)=0

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Solution for (8v+ux^2)(v-ux^2)=0 equation: 


Simplifying
(8v + ux2)(v + -1ux2) = 0

Reorder the terms:
(ux2 + 8v)(v + -1ux2) = 0

Reorder the terms:
(ux2 + 8v)(-1ux2 + v) = 0

Multiply (ux2 + 8v) * (-1ux2 + v)
(ux2(-1ux2 + v) + 8v * (-1ux2 + v)) = 0
((-1ux2 * ux2 + v * ux2) + 8v * (-1ux2 + v)) = 0

Reorder the terms:
((uvx2 + -1u2x4) + 8v * (-1ux2 + v)) = 0
((uvx2 + -1u2x4) + 8v * (-1ux2 + v)) = 0
(uvx2 + -1u2x4 + (-1ux2 * 8v + v * 8v)) = 0
(uvx2 + -1u2x4 + (-8uvx2 + 8v2)) = 0

Reorder the terms:
(uvx2 + -8uvx2 + -1u2x4 + 8v2) = 0

Combine like terms: uvx2 + -8uvx2 = -7uvx2
(-7uvx2 + -1u2x4 + 8v2) = 0

Solving
-7uvx2 + -1u2x4 + 8v2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-1ux2 + -8v)(ux2 + -1v) = 0


Subproblem 1
Set the factor '(-1ux2 + -8v)' equal to zero and attempt to solve:

Simplifying
-1ux2 + -8v = 0

Solving
-1ux2 + -8v = 0

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

Add '8v' to each side of the equation.
-1ux2 + -8v + 8v = 0 + 8v

Combine like terms: -8v + 8v = 0
-1ux2 + 0 = 0 + 8v
-1ux2 = 0 + 8v
Remove the zero:
-1ux2 = 8v

Divide each side by '-1x2'.
u = -8vx-2

Simplifying
u = -8vx-2

Subproblem 2
Set the factor '(ux2 + -1v)' equal to zero and attempt to solve:

Simplifying
ux2 + -1v = 0

Solving
ux2 + -1v = 0

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

Add 'v' to each side of the equation.
ux2 + -1v + v = 0 + v

Combine like terms: -1v + v = 0
ux2 + 0 = 0 + v
ux2 = 0 + v
Remove the zero:
ux2 = v

Divide each side by 'x2'.
u = vx-2

Simplifying
u = vx-2
Solution
u = {-8vx-2, vx-2}

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