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

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


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

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

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

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

Combine like terms: 2x + 4x = 6x
4x(8 + 6x + x2) = 0
(8 * 4x + 6x * 4x + x2 * 4x) = 0
(32x + 24x2 + 4x3) = 0

Solving
32x + 24x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(8 + 6x + x2) = 0

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

Ignore the factor 4.

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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