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

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

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

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

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

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

Combine like terms: 2u + 3u = 5u
(6 + 5u + u2) = 0

Solving
6 + 5u + u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(3 + u)(2 + u) = 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 '(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
Solution
u = {-3, -2}