(2u-1)(8+u)=0

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Solution for (2u-1)(8+u)=0 equation: 


Simplifying
(2u + -1)(8 + u) = 0

Reorder the terms:
(-1 + 2u)(8 + u) = 0

Multiply (-1 + 2u) * (8 + u)
(-1(8 + u) + 2u * (8 + u)) = 0
((8 * -1 + u * -1) + 2u * (8 + u)) = 0
((-8 + -1u) + 2u * (8 + u)) = 0
(-8 + -1u + (8 * 2u + u * 2u)) = 0
(-8 + -1u + (16u + 2u2)) = 0

Combine like terms: -1u + 16u = 15u
(-8 + 15u + 2u2) = 0

Solving
-8 + 15u + 2u2 = 0

Solving for variable 'u'.

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


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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