(2u+1)(3u+4)=0

Solution for (2u+1)(3u+4)=0 equation:

Simplifying
(2u + 1)(3u + 4) = 0

Reorder the terms:
(1 + 2u)(3u + 4) = 0

Reorder the terms:
(1 + 2u)(4 + 3u) = 0

Multiply (1 + 2u) * (4 + 3u)
(1(4 + 3u) + 2u * (4 + 3u)) = 0
((4 * 1 + 3u * 1) + 2u * (4 + 3u)) = 0
((4 + 3u) + 2u * (4 + 3u)) = 0
(4 + 3u + (4 * 2u + 3u * 2u)) = 0
(4 + 3u + (8u + 6u2)) = 0

Combine like terms: 3u + 8u = 11u
(4 + 11u + 6u2) = 0

Solving
4 + 11u + 6u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(4 + 3u)(1 + 2u) = 0

Subproblem 1
Set the factor '(4 + 3u)' equal to zero and attempt to solve:

Simplifying
4 + 3u = 0

Solving
4 + 3u = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3u = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3u = 0 + -4
3u = 0 + -4

Combine like terms: 0 + -4 = -4
3u = -4

Divide each side by '3'.
u = -1.333333333

Simplifying
u = -1.333333333
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 = {-1.333333333, -0.5}