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

Solution for (4+u)(5u-1)=0 equation:

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

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

Multiply (4 + u) * (-1 + 5u)
(4(-1 + 5u) + u(-1 + 5u)) = 0
((-1 * 4 + 5u * 4) + u(-1 + 5u)) = 0
((-4 + 20u) + u(-1 + 5u)) = 0
(-4 + 20u + (-1 * u + 5u * u)) = 0
(-4 + 20u + (-1u + 5u2)) = 0

Combine like terms: 20u + -1u = 19u
(-4 + 19u + 5u2) = 0

Solving
-4 + 19u + 5u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-4 + -1u)(1 + -5u) = 0

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

Simplifying
-4 + -1u = 0

Solving
-4 + -1u = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1u = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1u = 0 + 4
-1u = 0 + 4

Combine like terms: 0 + 4 = 4
-1u = 4

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

Simplifying
u = -4
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 = {-4, 0.2}