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

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Solution for x((2+(-1)x)(4+(-1)x))=0 equation: 


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

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

Combine like terms: -2x + -4x = -6x
x((8 + -6x + 1x2)) = 0
(8 * x + -6x * x + 1x2 * x) = 0
(8x + -6x2 + 1x3) = 0

Solving
8x + -6x2 + 1x3 = 0

Solving for variable 'x'.

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

Factor a trinomial.
x((2 + -1x)(4 + -1x)) = 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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 3
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
Solution
x = {0, 2, 4}

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