(x-1)*(2*x*x-2)*(x+3)=6

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Solution for (x-1)*(2*x*x-2)*(x+3)=6 equation: 


Simplifying
(x + -1)(2x * x + -2)(x + 3) = 6

Reorder the terms:
(-1 + x)(2x * x + -2)(x + 3) = 6

Multiply x * x
(-1 + x)(2x2 + -2)(x + 3) = 6

Reorder the terms:
(-1 + x)(-2 + 2x2)(x + 3) = 6

Reorder the terms:
(-1 + x)(-2 + 2x2)(3 + x) = 6

Multiply (-1 + x) * (-2 + 2x2)
(-1(-2 + 2x2) + x(-2 + 2x2))(3 + x) = 6
((-2 * -1 + 2x2 * -1) + x(-2 + 2x2))(3 + x) = 6
((2 + -2x2) + x(-2 + 2x2))(3 + x) = 6
(2 + -2x2 + (-2 * x + 2x2 * x))(3 + x) = 6
(2 + -2x2 + (-2x + 2x3))(3 + x) = 6

Reorder the terms:
(2 + -2x + -2x2 + 2x3)(3 + x) = 6
(2 + -2x + -2x2 + 2x3)(3 + x) = 6

Multiply (2 + -2x + -2x2 + 2x3) * (3 + x)
(2(3 + x) + -2x * (3 + x) + -2x2 * (3 + x) + 2x3 * (3 + x)) = 6
((3 * 2 + x * 2) + -2x * (3 + x) + -2x2 * (3 + x) + 2x3 * (3 + x)) = 6
((6 + 2x) + -2x * (3 + x) + -2x2 * (3 + x) + 2x3 * (3 + x)) = 6
(6 + 2x + (3 * -2x + x * -2x) + -2x2 * (3 + x) + 2x3 * (3 + x)) = 6
(6 + 2x + (-6x + -2x2) + -2x2 * (3 + x) + 2x3 * (3 + x)) = 6
(6 + 2x + -6x + -2x2 + (3 * -2x2 + x * -2x2) + 2x3 * (3 + x)) = 6
(6 + 2x + -6x + -2x2 + (-6x2 + -2x3) + 2x3 * (3 + x)) = 6
(6 + 2x + -6x + -2x2 + -6x2 + -2x3 + (3 * 2x3 + x * 2x3)) = 6
(6 + 2x + -6x + -2x2 + -6x2 + -2x3 + (6x3 + 2x4)) = 6

Combine like terms: 2x + -6x = -4x
(6 + -4x + -2x2 + -6x2 + -2x3 + 6x3 + 2x4) = 6

Combine like terms: -2x2 + -6x2 = -8x2
(6 + -4x + -8x2 + -2x3 + 6x3 + 2x4) = 6

Combine like terms: -2x3 + 6x3 = 4x3
(6 + -4x + -8x2 + 4x3 + 2x4) = 6

Add '-6' to each side of the equation.
6 + -4x + -8x2 + 4x3 + -6 + 2x4 = 6 + -6

Reorder the terms:
6 + -6 + -4x + -8x2 + 4x3 + 2x4 = 6 + -6

Combine like terms: 6 + -6 = 0
0 + -4x + -8x2 + 4x3 + 2x4 = 6 + -6
-4x + -8x2 + 4x3 + 2x4 = 6 + -6

Combine like terms: 6 + -6 = 0
-4x + -8x2 + 4x3 + 2x4 = 0

Solving
-4x + -8x2 + 4x3 + 2x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-2 + -4x + 2x2 + x3) = 0

Ignore the factor 2.

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 + -4x + 2x2 + x3)' equal to zero and attempt to solve:

Simplifying
-2 + -4x + 2x2 + x3 = 0

Solving
-2 + -4x + 2x2 + x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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