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

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Solution for 0=(x+0)(x+2)(x+4) equation: 


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

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

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

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

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

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

Solving
0 = 8x + 6x2 + x3

Solving for variable 'x'.
Remove the zero:
-8x + -6x2 + -1x3 = 8x + 6x2 + x3 + -8x + -6x2 + -1x3

Reorder the terms:
-8x + -6x2 + -1x3 = 8x + -8x + 6x2 + -6x2 + x3 + -1x3

Combine like terms: 8x + -8x = 0
-8x + -6x2 + -1x3 = 0 + 6x2 + -6x2 + x3 + -1x3
-8x + -6x2 + -1x3 = 6x2 + -6x2 + x3 + -1x3

Combine like terms: 6x2 + -6x2 = 0
-8x + -6x2 + -1x3 = 0 + x3 + -1x3
-8x + -6x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-8x + -6x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(8 + 6x + x2) = 0

Factor a trinomial.
-1x((4 + x)(2 + x)) = 0

Ignore the factor -1.

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}

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