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

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

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

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

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

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

Solving
-5 + -1u + 4u2 = 0

Solving for variable 'u'.

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

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

Simplifying
-1 + -1u = 0

Solving
-1 + -1u = 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 + -1u = 0 + 1

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

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

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

Simplifying
u = -1
Subproblem 2
Set the factor '(5 + -4u)' equal to zero and attempt to solve:

Simplifying
5 + -4u = 0

Solving
5 + -4u = 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 + -4u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4u = 0 + -5
-4u = 0 + -5

Combine like terms: 0 + -5 = -5
-4u = -5

Divide each side by '-4'.
u = 1.25

Simplifying
u = 1.25
Solution
u = {-1, 1.25}