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

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

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

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

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