(8+u)(4u-2)=0

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Solution for (8+u)(4u-2)=0 equation: 


Simplifying
(8 + u)(4u + -2) = 0

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

Multiply (8 + u) * (-2 + 4u)
(8(-2 + 4u) + u(-2 + 4u)) = 0
((-2 * 8 + 4u * 8) + u(-2 + 4u)) = 0
((-16 + 32u) + u(-2 + 4u)) = 0
(-16 + 32u + (-2 * u + 4u * u)) = 0
(-16 + 32u + (-2u + 4u2)) = 0

Combine like terms: 32u + -2u = 30u
(-16 + 30u + 4u2) = 0

Solving
-16 + 30u + 4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 15u + 2u2) = 0

Factor a trinomial.
2((-8 + -1u)(1 + -2u)) = 0

Ignore the factor 2.

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

Simplifying
-8 + -1u = 0

Solving
-8 + -1u = 0

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

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

Combine like terms: -8 + 8 = 0
0 + -1u = 0 + 8
-1u = 0 + 8

Combine like terms: 0 + 8 = 8
-1u = 8

Divide each side by '-1'.
u = -8

Simplifying
u = -8

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

Simplifying
1 + -2u = 0

Solving
1 + -2u = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2u = 0 + -1
-2u = 0 + -1

Combine like terms: 0 + -1 = -1
-2u = -1

Divide each side by '-2'.
u = 0.5

Simplifying
u = 0.5
Solution
u = {-8, 0.5}

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