(4u+2)(9+u)=0

Solution for (4u+2)(9+u)=0 equation:

Simplifying
(4u + 2)(9 + u) = 0

Reorder the terms:
(2 + 4u)(9 + u) = 0

Multiply (2 + 4u) * (9 + u)
(2(9 + u) + 4u * (9 + u)) = 0
((9 * 2 + u * 2) + 4u * (9 + u)) = 0
((18 + 2u) + 4u * (9 + u)) = 0
(18 + 2u + (9 * 4u + u * 4u)) = 0
(18 + 2u + (36u + 4u2)) = 0

Combine like terms: 2u + 36u = 38u
(18 + 38u + 4u2) = 0

Solving
18 + 38u + 4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 19u + 2u2) = 0

Factor a trinomial.
2((9 + u)(1 + 2u)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(9 + u)' equal to zero and attempt to solve:

Simplifying
9 + u = 0

Solving
9 + u = 0

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

Add '-9' to each side of the equation.
9 + -9 + u = 0 + -9

Combine like terms: 9 + -9 = 0
0 + u = 0 + -9
u = 0 + -9

Combine like terms: 0 + -9 = -9
u = -9

Simplifying
u = -9
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 = {-9, -0.5}