(2u+1)(9u-5)=0

Solution for (2u+1)(9u-5)=0 equation:

Simplifying
(2u + 1)(9u + -5) = 0

Reorder the terms:
(1 + 2u)(9u + -5) = 0

Reorder the terms:
(1 + 2u)(-5 + 9u) = 0

Multiply (1 + 2u) * (-5 + 9u)
(1(-5 + 9u) + 2u * (-5 + 9u)) = 0
((-5 * 1 + 9u * 1) + 2u * (-5 + 9u)) = 0
((-5 + 9u) + 2u * (-5 + 9u)) = 0
(-5 + 9u + (-5 * 2u + 9u * 2u)) = 0
(-5 + 9u + (-10u + 18u2)) = 0

Combine like terms: 9u + -10u = -1u
(-5 + -1u + 18u2) = 0

Solving
-5 + -1u + 18u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-1 + -2u)(5 + -9u) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -9u)' equal to zero and attempt to solve:

Simplifying
5 + -9u = 0

Solving
5 + -9u = 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 + -9u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -9u = 0 + -5
-9u = 0 + -5

Combine like terms: 0 + -5 = -5
-9u = -5

Divide each side by '-9'.
u = 0.5555555556

Simplifying
u = 0.5555555556
Solution
u = {-0.5, 0.5555555556}