(4u+7)(1+u)=0

Solution for (4u+7)(1+u)=0 equation:

Simplifying
(4u + 7)(1 + u) = 0

Reorder the terms:
(7 + 4u)(1 + u) = 0

Multiply (7 + 4u) * (1 + u)
(7(1 + u) + 4u * (1 + u)) = 0
((1 * 7 + u * 7) + 4u * (1 + u)) = 0
((7 + 7u) + 4u * (1 + u)) = 0
(7 + 7u + (1 * 4u + u * 4u)) = 0
(7 + 7u + (4u + 4u2)) = 0

Combine like terms: 7u + 4u = 11u
(7 + 11u + 4u2) = 0

Solving
7 + 11u + 4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(7 + 4u)(1 + u) = 0

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

Simplifying
1 + u = 0

Solving
1 + u = 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 + u = 0 + -1

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

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

Simplifying
u = -1
Solution
u = {-1.75, -1}