x(x+2)(x+6)=0

Solution for x(x+2)(x+6)=0 equation:

Simplifying
x(x + 2)(x + 6) = 0

Reorder the terms:
x(2 + x)(x + 6) = 0

Reorder the terms:
x(2 + x)(6 + x) = 0

Multiply (2 + x) * (6 + x)
x(2(6 + x) + x(6 + x)) = 0
x((6 * 2 + x * 2) + x(6 + x)) = 0
x((12 + 2x) + x(6 + x)) = 0
x(12 + 2x + (6 * x + x * x)) = 0
x(12 + 2x + (6x + x2)) = 0

Combine like terms: 2x + 6x = 8x
x(12 + 8x + x2) = 0
(12 * x + 8x * x + x2 * x) = 0
(12x + 8x2 + x3) = 0

Solving
12x + 8x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(12 + 8x + x2) = 0

Factor a trinomial.
x((6 + x)(2 + 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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {0, -6, -2}