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

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


Simplifying
x(4 + -1x)(2 + x) = 0

Multiply (4 + -1x) * (2 + x)
x(4(2 + x) + -1x * (2 + x)) = 0
x((2 * 4 + x * 4) + -1x * (2 + x)) = 0
x((8 + 4x) + -1x * (2 + x)) = 0
x(8 + 4x + (2 * -1x + x * -1x)) = 0
x(8 + 4x + (-2x + -1x2)) = 0

Combine like terms: 4x + -2x = 2x
x(8 + 2x + -1x2) = 0
(8 * x + 2x * x + -1x2 * x) = 0
(8x + 2x2 + -1x3) = 0

Solving
8x + 2x2 + -1x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(8 + 2x + -1x2) = 0

Factor a trinomial.
x((4 + -1x)(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 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
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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