5u(u+1)(u+3)=0

Solution for 5u(u+1)(u+3)=0 equation:

Simplifying
5u(u + 1)(u + 3) = 0

Reorder the terms:
5u(1 + u)(u + 3) = 0

Reorder the terms:
5u(1 + u)(3 + u) = 0

Multiply (1 + u) * (3 + u)
5u(1(3 + u) + u(3 + u)) = 0
5u((3 * 1 + u * 1) + u(3 + u)) = 0
5u((3 + 1u) + u(3 + u)) = 0
5u(3 + 1u + (3 * u + u * u)) = 0
5u(3 + 1u + (3u + u2)) = 0

Combine like terms: 1u + 3u = 4u
5u(3 + 4u + u2) = 0
(3 * 5u + 4u * 5u + u2 * 5u) = 0
(15u + 20u2 + 5u3) = 0

Solving
15u + 20u2 + 5u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '5u'.
5u(3 + 4u + u2) = 0

Factor a trinomial.
5u((3 + u)(1 + 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 '(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 = {0, -3, -1}