(x-1)(x^2+x-2)=x^2+2

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

Simplifying
(x + -1)(x2 + x + -2) = x2 + 2

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

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

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

Reorder the terms:
(2 + -1x + -2x + -1x2 + x2 + x3) = x2 + 2

Combine like terms: -1x + -2x = -3x
(2 + -3x + -1x2 + x2 + x3) = x2 + 2

Combine like terms: -1x2 + x2 = 0
(2 + -3x + 0 + x3) = x2 + 2
(2 + -3x + x3) = x2 + 2

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

Add '-2' to each side of the equation.
2 + -3x + -2 + x3 = 2 + -2 + x2

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

Combine like terms: 2 + -2 = 0
0 + -3x + x3 = 2 + -2 + x2
-3x + x3 = 2 + -2 + x2

Combine like terms: 2 + -2 = 0
-3x + x3 = 0 + x2
-3x + x3 = x2

Solving
-3x + x3 = x2

Solving for variable 'x'.

Reorder the terms:
-3x + -1x2 + x3 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-3x + -1x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-3 + -1x + x2) = 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 '(-3 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
-3 + -1x + x2 = 0

Solving
-3 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -1x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -1x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x + x2 = 0 + 3
-1x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1x + x2 = 3

The x term is -1x.  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.
-1x + 0.25 + x2 = 3 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 3 + 0.25

Combine like terms: 3 + 0.25 = 3.25
0.25 + -1x + x2 = 3.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
x + -0.5 = 1.802775638

Simplifying
x + -0.5 = 1.802775638

Reorder the terms:
-0.5 + x = 1.802775638

Solving
-0.5 + x = 1.802775638

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 = 1.802775638 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 1.802775638 + 0.5
x = 1.802775638 + 0.5

Combine like terms: 1.802775638 + 0.5 = 2.302775638
x = 2.302775638

Simplifying
x = 2.302775638

Subproblem 2
x + -0.5 = -1.802775638

Simplifying
x + -0.5 = -1.802775638

Reorder the terms:
-0.5 + x = -1.802775638

Solving
-0.5 + x = -1.802775638

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 = -1.802775638 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -1.802775638 + 0.5
x = -1.802775638 + 0.5

Combine like terms: -1.802775638 + 0.5 = -1.302775638
x = -1.302775638

Simplifying
x = -1.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.302775638, -1.302775638}
Solution
x = {0, 2.302775638, -1.302775638}