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

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

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

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

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

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

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

Solving
-20 + 1u + u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-5 + -1u)(4 + -1u) = 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 '(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
Solution
u = {-5, 4}