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

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

Simplifying
(4u + 2)(5 + -1u) = 0

Reorder the terms:
(2 + 4u)(5 + -1u) = 0

Multiply (2 + 4u) * (5 + -1u)
(2(5 + -1u) + 4u * (5 + -1u)) = 0
((5 * 2 + -1u * 2) + 4u * (5 + -1u)) = 0
((10 + -2u) + 4u * (5 + -1u)) = 0
(10 + -2u + (5 * 4u + -1u * 4u)) = 0
(10 + -2u + (20u + -4u2)) = 0

Combine like terms: -2u + 20u = 18u
(10 + 18u + -4u2) = 0

Solving
10 + 18u + -4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 9u + -2u2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + -1u)' equal to zero and attempt to solve:

Simplifying
5 + -1u = 0

Solving
5 + -1u = 0

Move all terms containing u to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1u = 0 + -5
-1u = 0 + -5

Combine like terms: 0 + -5 = -5
-1u = -5

Divide each side by '-1'.
u = 5

Simplifying
u = 5
Subproblem 2
Set the factor '(1 + 2u)' equal to zero and attempt to solve:

Simplifying
1 + 2u = 0

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

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

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

Divide each side by '2'.
u = -0.5

Simplifying
u = -0.5
Solution
u = {5, -0.5}