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

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

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

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

Multiply (1 + 5u) * (5 + -1u)
(1(5 + -1u) + 5u * (5 + -1u)) = 0
((5 * 1 + -1u * 1) + 5u * (5 + -1u)) = 0
((5 + -1u) + 5u * (5 + -1u)) = 0
(5 + -1u + (5 * 5u + -1u * 5u)) = 0
(5 + -1u + (25u + -5u2)) = 0

Combine like terms: -1u + 25u = 24u
(5 + 24u + -5u2) = 0

Solving
5 + 24u + -5u2 = 0

Solving for variable 'u'.

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

Subproblem 1
Set the factor '(5 + -1u)' equal to zero and attempt to solve:

Simplifying
5 + -1u = 0

Solving
5 + -1u = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1u = 0 + -5

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

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

Divide each side by '-1'.
u = 5

Simplifying
u = 5
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 = {5, -0.2}