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

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

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

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

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

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

Solving
6 + 11u + 4u2 = 0

Solving for variable 'u'.

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

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

Simplifying
2 + u = 0

Solving
2 + u = 0

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

Add '-2' to each side of the equation.
2 + -2 + u = 0 + -2

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

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

Simplifying
u = -2
Subproblem 2
Set the factor '(3 + 4u)' equal to zero and attempt to solve:

Simplifying
3 + 4u = 0

Solving
3 + 4u = 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 + 4u = 0 + -3

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

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

Divide each side by '4'.
u = -0.75

Simplifying
u = -0.75
Solution
u = {-2, -0.75}