4u(u+5)(u+6)=0

Solution for 4u(u+5)(u+6)=0 equation:

Simplifying
4u(u + 5)(u + 6) = 0

Reorder the terms:
4u(5 + u)(u + 6) = 0

Reorder the terms:
4u(5 + u)(6 + u) = 0

Multiply (5 + u) * (6 + u)
4u(5(6 + u) + u(6 + u)) = 0
4u((6 * 5 + u * 5) + u(6 + u)) = 0
4u((30 + 5u) + u(6 + u)) = 0
4u(30 + 5u + (6 * u + u * u)) = 0
4u(30 + 5u + (6u + u2)) = 0

Combine like terms: 5u + 6u = 11u
4u(30 + 11u + u2) = 0
(30 * 4u + 11u * 4u + u2 * 4u) = 0
(120u + 44u2 + 4u3) = 0

Solving
120u + 44u2 + 4u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '4u'.
4u(30 + 11u + u2) = 0

Factor a trinomial.
4u((6 + u)(5 + u)) = 0

Ignore the factor 4.
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 '(6 + u)' equal to zero and attempt to solve:

Simplifying
6 + u = 0

Solving
6 + u = 0

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

Add '-6' to each side of the equation.
6 + -6 + u = 0 + -6

Combine like terms: 6 + -6 = 0
0 + u = 0 + -6
u = 0 + -6

Combine like terms: 0 + -6 = -6
u = -6

Simplifying
u = -6
Subproblem 3
Set the factor '(5 + u)' equal to zero and attempt to solve:

Simplifying
5 + u = 0

Solving
5 + u = 0

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

Add '-5' to each side of the equation.
5 + -5 + u = 0 + -5

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

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

Simplifying
u = -5
Solution
u = {0, -6, -5}