(2u-bn)(4u-bn)=

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Solution for (2u-bn)(4u-bn)= equation: 


Simplifying
(2u + -1bn)(4u + -1bn) = 0

Reorder the terms:
(-1bn + 2u)(4u + -1bn) = 0

Reorder the terms:
(-1bn + 2u)(-1bn + 4u) = 0

Multiply (-1bn + 2u) * (-1bn + 4u)
(-1bn * (-1bn + 4u) + 2u * (-1bn + 4u)) = 0
((-1bn * -1bn + 4u * -1bn) + 2u * (-1bn + 4u)) = 0

Reorder the terms:
((-4bnu + 1b2n2) + 2u * (-1bn + 4u)) = 0
((-4bnu + 1b2n2) + 2u * (-1bn + 4u)) = 0
(-4bnu + 1b2n2 + (-1bn * 2u + 4u * 2u)) = 0
(-4bnu + 1b2n2 + (-2bnu + 8u2)) = 0

Reorder the terms:
(-4bnu + -2bnu + 1b2n2 + 8u2) = 0

Combine like terms: -4bnu + -2bnu = -6bnu
(-6bnu + 1b2n2 + 8u2) = 0

Solving
-6bnu + 1b2n2 + 8u2 = 0

Solving for variable 'b'.

Factor a trinomial.
(bn + -4u)(bn + -2u) = 0


Subproblem 1
Set the factor '(bn + -4u)' equal to zero and attempt to solve:

Simplifying
bn + -4u = 0

Solving
bn + -4u = 0

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

Add '4u' to each side of the equation.
bn + -4u + 4u = 0 + 4u

Combine like terms: -4u + 4u = 0
bn + 0 = 0 + 4u
bn = 0 + 4u
Remove the zero:
bn = 4u

Divide each side by 'n'.
b = 4n-1u

Simplifying
b = 4n-1u

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

Simplifying
bn + -2u = 0

Solving
bn + -2u = 0

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

Add '2u' to each side of the equation.
bn + -2u + 2u = 0 + 2u

Combine like terms: -2u + 2u = 0
bn + 0 = 0 + 2u
bn = 0 + 2u
Remove the zero:
bn = 2u

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

Simplifying
b = 2n-1u
Solution
b = {4n-1u, 2n-1u}

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