(8+u)(5u-1)=0

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Solution for (8+u)(5u-1)=0 equation: 


Simplifying
(8 + u)(5u + -1) = 0

Reorder the terms:
(8 + u)(-1 + 5u) = 0

Multiply (8 + u) * (-1 + 5u)
(8(-1 + 5u) + u(-1 + 5u)) = 0
((-1 * 8 + 5u * 8) + u(-1 + 5u)) = 0
((-8 + 40u) + u(-1 + 5u)) = 0
(-8 + 40u + (-1 * u + 5u * u)) = 0
(-8 + 40u + (-1u + 5u2)) = 0

Combine like terms: 40u + -1u = 39u
(-8 + 39u + 5u2) = 0

Solving
-8 + 39u + 5u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-8 + -1u)(1 + -5u) = 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 + -5u)' equal to zero and attempt to solve:

Simplifying
1 + -5u = 0

Solving
1 + -5u = 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 + -5u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5u = 0 + -1
-5u = 0 + -1

Combine like terms: 0 + -1 = -1
-5u = -1

Divide each side by '-5'.
u = 0.2

Simplifying
u = 0.2
Solution
u = {-8, 0.2}

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