(5-u)(5u+2)=0

Solution for (5-u)(5u+2)=0 equation:

Simplifying
(5 + -1u)(5u + 2) = 0

Reorder the terms:
(5 + -1u)(2 + 5u) = 0

Multiply (5 + -1u) * (2 + 5u)
(5(2 + 5u) + -1u * (2 + 5u)) = 0
((2 * 5 + 5u * 5) + -1u * (2 + 5u)) = 0
((10 + 25u) + -1u * (2 + 5u)) = 0
(10 + 25u + (2 * -1u + 5u * -1u)) = 0
(10 + 25u + (-2u + -5u2)) = 0

Combine like terms: 25u + -2u = 23u
(10 + 23u + -5u2) = 0

Solving
10 + 23u + -5u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(5 + -1u)(2 + 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 '(2 + 5u)' equal to zero and attempt to solve:

Simplifying
2 + 5u = 0

Solving
2 + 5u = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5u = 0 + -2
5u = 0 + -2

Combine like terms: 0 + -2 = -2
5u = -2

Divide each side by '5'.
u = -0.4

Simplifying
u = -0.4
Solution
u = {5, -0.4}