(2u-1)(3+u)=0

Solution for (2u-1)(3+u)=0 equation:

Simplifying
(2u + -1)(3 + u) = 0

Reorder the terms:
(-1 + 2u)(3 + u) = 0

Multiply (-1 + 2u) * (3 + u)
(-1(3 + u) + 2u * (3 + u)) = 0
((3 * -1 + u * -1) + 2u * (3 + u)) = 0
((-3 + -1u) + 2u * (3 + u)) = 0
(-3 + -1u + (3 * 2u + u * 2u)) = 0
(-3 + -1u + (6u + 2u2)) = 0

Combine like terms: -1u + 6u = 5u
(-3 + 5u + 2u2) = 0

Solving
-3 + 5u + 2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-3 + -1u)(1 + -2u) = 0

Subproblem 1
Set the factor '(-3 + -1u)' equal to zero and attempt to solve:

Simplifying
-3 + -1u = 0

Solving
-3 + -1u = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1u = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1u = 0 + 3
-1u = 0 + 3

Combine like terms: 0 + 3 = 3
-1u = 3

Divide each side by '-1'.
u = -3

Simplifying
u = -3
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 = {-3, 0.5}