x(x+2)(x+4)=

Solution for x(x+2)(x+4)= equation:

Simplifying
x(x + 2)(x + 4) = 0

Reorder the terms:
x(2 + x)(x + 4) = 0

Reorder the terms:
x(2 + x)(4 + x) = 0

Multiply (2 + x) * (4 + x)
x(2(4 + x) + x(4 + x)) = 0
x((4 * 2 + x * 2) + x(4 + x)) = 0
x((8 + 2x) + x(4 + x)) = 0
x(8 + 2x + (4 * x + x * x)) = 0
x(8 + 2x + (4x + x2)) = 0

Combine like terms: 2x + 4x = 6x
x(8 + 6x + x2) = 0
(8 * x + 6x * x + x2 * x) = 0
(8x + 6x2 + x3) = 0

Solving
8x + 6x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(8 + 6x + x2) = 0

Factor a trinomial.
x((4 + 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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
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, -4, -2}