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

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

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

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

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

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

Combine like terms: 3u + 7u = 10u
(21 + 10u + u2) = 0

Solving
21 + 10u + u2 = 0

Solving for variable 'u'.

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

Subproblem 1
Set the factor '(7 + u)' equal to zero and attempt to solve:

Simplifying
7 + u = 0

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

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

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

Simplifying
u = -7
Subproblem 2
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
Solution
u = {-7, -3}