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

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


Simplifying
2x2(x + 4)(x + 2) = 0

Reorder the terms:
2x2(4 + x)(x + 2) = 0

Reorder the terms:
2x2(4 + x)(2 + x) = 0

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

Combine like terms: 4x + 2x = 6x
2x2(8 + 6x + x2) = 0
(8 * 2x2 + 6x * 2x2 + x2 * 2x2) = 0
(16x2 + 12x3 + 2x4) = 0

Solving
16x2 + 12x3 + 2x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(8 + 6x + x2) = 0

Factor a trinomial.
2x2((4 + x)(2 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
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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