5u(u+3)(u+2)=0

Solution for 5u(u+3)(u+2)=0 equation:

Simplifying
5u(u + 3)(u + 2) = 0

Reorder the terms:
5u(3 + u)(u + 2) = 0

Reorder the terms:
5u(3 + u)(2 + u) = 0

Multiply (3 + u) * (2 + u)
5u(3(2 + u) + u(2 + u)) = 0
5u((2 * 3 + u * 3) + u(2 + u)) = 0
5u((6 + 3u) + u(2 + u)) = 0
5u(6 + 3u + (2 * u + u * u)) = 0
5u(6 + 3u + (2u + u2)) = 0

Combine like terms: 3u + 2u = 5u
5u(6 + 5u + u2) = 0
(6 * 5u + 5u * 5u + u2 * 5u) = 0
(30u + 25u2 + 5u3) = 0

Solving
30u + 25u2 + 5u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '5u'.
5u(6 + 5u + u2) = 0

Factor a trinomial.
5u((3 + u)(2 + u)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'u' equal to zero and attempt to solve:

Simplifying
u = 0

Solving
u = 0

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

Simplifying
u = 0
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
Subproblem 3
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 = {0, -3, -2}