x(x+6)(x+5)=0

Solution for x(x+6)(x+5)=0 equation:

Simplifying
x(x + 6)(x + 5) = 0

Reorder the terms:
x(6 + x)(x + 5) = 0

Reorder the terms:
x(6 + x)(5 + x) = 0

Multiply (6 + x) * (5 + x)
x(6(5 + x) + x(5 + x)) = 0
x((5 * 6 + x * 6) + x(5 + x)) = 0
x((30 + 6x) + x(5 + x)) = 0
x(30 + 6x + (5 * x + x * x)) = 0
x(30 + 6x + (5x + x2)) = 0

Combine like terms: 6x + 5x = 11x
x(30 + 11x + x2) = 0
(30 * x + 11x * x + x2 * x) = 0
(30x + 11x2 + x3) = 0

Solving
30x + 11x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(30 + 11x + x2) = 0

Factor a trinomial.
x((6 + x)(5 + x)) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

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

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

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

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

Simplifying
5 + x = 0

Solving
5 + x = 0

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

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

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

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

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