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

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

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

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

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

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

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

Combine like terms: -2x + -2x = -4x
(2 + -4x + 2x2)(3 + x) = 6

Multiply (2 + -4x + 2x2) * (3 + x)
(2(3 + x) + -4x * (3 + x) + 2x2 * (3 + x)) = 6
((3 * 2 + x * 2) + -4x * (3 + x) + 2x2 * (3 + x)) = 6
((6 + 2x) + -4x * (3 + x) + 2x2 * (3 + x)) = 6
(6 + 2x + (3 * -4x + x * -4x) + 2x2 * (3 + x)) = 6
(6 + 2x + (-12x + -4x2) + 2x2 * (3 + x)) = 6
(6 + 2x + -12x + -4x2 + (3 * 2x2 + x * 2x2)) = 6
(6 + 2x + -12x + -4x2 + (6x2 + 2x3)) = 6

Combine like terms: 2x + -12x = -10x
(6 + -10x + -4x2 + 6x2 + 2x3) = 6

Combine like terms: -4x2 + 6x2 = 2x2
(6 + -10x + 2x2 + 2x3) = 6

Add '-6' to each side of the equation.
6 + -10x + 2x2 + -6 + 2x3 = 6 + -6

Reorder the terms:
6 + -6 + -10x + 2x2 + 2x3 = 6 + -6

Combine like terms: 6 + -6 = 0
0 + -10x + 2x2 + 2x3 = 6 + -6
-10x + 2x2 + 2x3 = 6 + -6

Combine like terms: 6 + -6 = 0
-10x + 2x2 + 2x3 = 0

Solving
-10x + 2x2 + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-5 + x + x2) = 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 '(-5 + x + x2)' equal to zero and attempt to solve:

Simplifying
-5 + x + x2 = 0

Solving
-5 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x + x2 = 0 + 5
x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
x + x2 = 5

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 5 + 0.25

Reorder the terms:
0.25 + x + x2 = 5 + 0.25

Combine like terms: 5 + 0.25 = 5.25
0.25 + x + x2 = 5.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.291287847 and -2.291287847.

Subproblem 1
x + 0.5 = 2.291287847

Simplifying
x + 0.5 = 2.291287847

Reorder the terms:
0.5 + x = 2.291287847

Solving
0.5 + x = 2.291287847

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 2.291287847 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.291287847 + -0.5
x = 2.291287847 + -0.5

Combine like terms: 2.291287847 + -0.5 = 1.791287847
x = 1.791287847

Simplifying
x = 1.791287847

Subproblem 2
x + 0.5 = -2.291287847

Simplifying
x + 0.5 = -2.291287847

Reorder the terms:
0.5 + x = -2.291287847

Solving
0.5 + x = -2.291287847

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -2.291287847 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.291287847 + -0.5
x = -2.291287847 + -0.5

Combine like terms: -2.291287847 + -0.5 = -2.791287847
x = -2.791287847

Simplifying
x = -2.791287847

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.791287847, -2.791287847}
Solution
x = {0, 1.791287847, -2.791287847}