(v+bu^2)(5v+3bu^2)=0

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Solution for (v+bu^2)(5v+3bu^2)=0 equation: 


Simplifying
(v + bu2)(5v + 3bu2) = 0

Reorder the terms:
(bu2 + v)(5v + 3bu2) = 0

Reorder the terms:
(bu2 + v)(3bu2 + 5v) = 0

Multiply (bu2 + v) * (3bu2 + 5v)
(bu2(3bu2 + 5v) + v(3bu2 + 5v)) = 0
((3bu2 * bu2 + 5v * bu2) + v(3bu2 + 5v)) = 0

Reorder the terms:
((5bu2v + 3b2u4) + v(3bu2 + 5v)) = 0
((5bu2v + 3b2u4) + v(3bu2 + 5v)) = 0
(5bu2v + 3b2u4 + (3bu2 * v + 5v * v)) = 0
(5bu2v + 3b2u4 + (3bu2v + 5v2)) = 0

Reorder the terms:
(5bu2v + 3bu2v + 3b2u4 + 5v2) = 0

Combine like terms: 5bu2v + 3bu2v = 8bu2v
(8bu2v + 3b2u4 + 5v2) = 0

Solving
8bu2v + 3b2u4 + 5v2 = 0

Solving for variable 'b'.

Factor a trinomial.
(bu2 + v)(3bu2 + 5v) = 0


Subproblem 1
Set the factor '(bu2 + v)' equal to zero and attempt to solve:

Simplifying
bu2 + v = 0

Solving
bu2 + v = 0

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

Add '-1v' to each side of the equation.
bu2 + v + -1v = 0 + -1v

Combine like terms: v + -1v = 0
bu2 + 0 = 0 + -1v
bu2 = 0 + -1v
Remove the zero:
bu2 = -1v

Divide each side by 'u2'.
b = -1u-2v

Simplifying
b = -1u-2v

Subproblem 2
Set the factor '(3bu2 + 5v)' equal to zero and attempt to solve:

Simplifying
3bu2 + 5v = 0

Solving
3bu2 + 5v = 0

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

Add '-5v' to each side of the equation.
3bu2 + 5v + -5v = 0 + -5v

Combine like terms: 5v + -5v = 0
3bu2 + 0 = 0 + -5v
3bu2 = 0 + -5v
Remove the zero:
3bu2 = -5v

Divide each side by '3u2'.
b = -1.666666667u-2v

Simplifying
b = -1.666666667u-2v
Solution
b = {-1u-2v, -1.666666667u-2v}

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