(3+u)(5u+7)=0

Solution for (3+u)(5u+7)=0 equation:

Simplifying
(3 + u)(5u + 7) = 0

Reorder the terms:
(3 + u)(7 + 5u) = 0

Multiply (3 + u) * (7 + 5u)
(3(7 + 5u) + u(7 + 5u)) = 0
((7 * 3 + 5u * 3) + u(7 + 5u)) = 0
((21 + 15u) + u(7 + 5u)) = 0
(21 + 15u + (7 * u + 5u * u)) = 0
(21 + 15u + (7u + 5u2)) = 0

Combine like terms: 15u + 7u = 22u
(21 + 22u + 5u2) = 0

Solving
21 + 22u + 5u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(3 + u)(7 + 5u) = 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 + 5u)' equal to zero and attempt to solve:

Simplifying
7 + 5u = 0

Solving
7 + 5u = 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 + 5u = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 5u = 0 + -7
5u = 0 + -7

Combine like terms: 0 + -7 = -7
5u = -7

Divide each side by '5'.
u = -1.4

Simplifying
u = -1.4
Solution
u = {-3, -1.4}