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

Solution for (2+u)(5u-4)=0 equation:

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

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

Multiply (2 + u) * (-4 + 5u)
(2(-4 + 5u) + u(-4 + 5u)) = 0
((-4 * 2 + 5u * 2) + u(-4 + 5u)) = 0
((-8 + 10u) + u(-4 + 5u)) = 0
(-8 + 10u + (-4 * u + 5u * u)) = 0
(-8 + 10u + (-4u + 5u2)) = 0

Combine like terms: 10u + -4u = 6u
(-8 + 6u + 5u2) = 0

Solving
-8 + 6u + 5u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-2 + -1u)(4 + -5u) = 0

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

Simplifying
-2 + -1u = 0

Solving
-2 + -1u = 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 + -1u = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1u = 0 + 2
-1u = 0 + 2

Combine like terms: 0 + 2 = 2
-1u = 2

Divide each side by '-1'.
u = -2

Simplifying
u = -2
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 = {-2, 0.8}