(4u+7)(3+u)=0

Solution for (4u+7)(3+u)=0 equation:

Simplifying
(4u + 7)(3 + u) = 0

Reorder the terms:
(7 + 4u)(3 + u) = 0

Multiply (7 + 4u) * (3 + u)
(7(3 + u) + 4u * (3 + u)) = 0
((3 * 7 + u * 7) + 4u * (3 + u)) = 0
((21 + 7u) + 4u * (3 + u)) = 0
(21 + 7u + (3 * 4u + u * 4u)) = 0
(21 + 7u + (12u + 4u2)) = 0

Combine like terms: 7u + 12u = 19u
(21 + 19u + 4u2) = 0

Solving
21 + 19u + 4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(3 + u)(7 + 4u) = 0

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

Simplifying
3 + u = 0

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

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

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

Simplifying
u = -3
Subproblem 2
Set the factor '(7 + 4u)' equal to zero and attempt to solve:

Simplifying
7 + 4u = 0

Solving
7 + 4u = 0

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

Add '-7' to each side of the equation.
7 + -7 + 4u = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4u = 0 + -7
4u = 0 + -7

Combine like terms: 0 + -7 = -7
4u = -7

Divide each side by '4'.
u = -1.75

Simplifying
u = -1.75
Solution
u = {-3, -1.75}