(u-5)(u+3)=0

Solution for (u-5)(u+3)=0 equation:

Simplifying
(u + -5)(u + 3) = 0

Reorder the terms:
(-5 + u)(u + 3) = 0

Reorder the terms:
(-5 + u)(3 + u) = 0

Multiply (-5 + u) * (3 + u)
(-5(3 + u) + u(3 + u)) = 0
((3 * -5 + u * -5) + u(3 + u)) = 0
((-15 + -5u) + u(3 + u)) = 0
(-15 + -5u + (3 * u + u * u)) = 0
(-15 + -5u + (3u + u2)) = 0

Combine like terms: -5u + 3u = -2u
(-15 + -2u + u2) = 0

Solving
-15 + -2u + u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-3 + -1u)(5 + -1u) = 0

Subproblem 1
Set the factor '(-3 + -1u)' equal to zero and attempt to solve:

Simplifying
-3 + -1u = 0

Solving
-3 + -1u = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1u = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1u = 0 + 3
-1u = 0 + 3

Combine like terms: 0 + 3 = 3
-1u = 3

Divide each side by '-1'.
u = -3

Simplifying
u = -3
Subproblem 2
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
Solution
u = {-3, 5}