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

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


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

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

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