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

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

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

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

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

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

Solving
-4 + 1u + 5u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-1 + -1u)(4 + -5u) = 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 '(4 + -5u)' equal to zero and attempt to solve:

Simplifying
4 + -5u = 0

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

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

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

Divide each side by '-5'.
u = 0.8

Simplifying
u = 0.8
Solution
u = {-1, 0.8}