(4u-1)(2+u)=0

Solution for (4u-1)(2+u)=0 equation:

Simplifying
(4u + -1)(2 + u) = 0

Reorder the terms:
(-1 + 4u)(2 + u) = 0

Multiply (-1 + 4u) * (2 + u)
(-1(2 + u) + 4u * (2 + u)) = 0
((2 * -1 + u * -1) + 4u * (2 + u)) = 0
((-2 + -1u) + 4u * (2 + u)) = 0
(-2 + -1u + (2 * 4u + u * 4u)) = 0
(-2 + -1u + (8u + 4u2)) = 0

Combine like terms: -1u + 8u = 7u
(-2 + 7u + 4u2) = 0

Solving
-2 + 7u + 4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-2 + -1u)(1 + -4u) = 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 '(1 + -4u)' equal to zero and attempt to solve:

Simplifying
1 + -4u = 0

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

Combine like terms: 1 + -1 = 0
0 + -4u = 0 + -1
-4u = 0 + -1

Combine like terms: 0 + -1 = -1
-4u = -1

Divide each side by '-4'.
u = 0.25

Simplifying
u = 0.25
Solution
u = {-2, 0.25}