(5u-2)(1+u)=0

Solution for (5u-2)(1+u)=0 equation:

Simplifying
(5u + -2)(1 + u) = 0

Reorder the terms:
(-2 + 5u)(1 + u) = 0

Multiply (-2 + 5u) * (1 + u)
(-2(1 + u) + 5u * (1 + u)) = 0
((1 * -2 + u * -2) + 5u * (1 + u)) = 0
((-2 + -2u) + 5u * (1 + u)) = 0
(-2 + -2u + (1 * 5u + u * 5u)) = 0
(-2 + -2u + (5u + 5u2)) = 0

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

Solving
-2 + 3u + 5u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-1 + -1u)(2 + -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 '(2 + -5u)' equal to zero and attempt to solve:

Simplifying
2 + -5u = 0

Solving
2 + -5u = 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 + -5u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5u = 0 + -2
-5u = 0 + -2

Combine like terms: 0 + -2 = -2
-5u = -2

Divide each side by '-5'.
u = 0.4

Simplifying
u = 0.4
Solution
u = {-1, 0.4}