x^3+2x^2-6x+2=x(x^2-2)

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


Simplifying
x3 + 2x2 + -6x + 2 = x(x2 + -2)

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

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

Add '-1x3' to each side of the equation.
2 + -6x + 2x2 + x3 + -1x3 = -2x + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
2 + -6x + 2x2 + 0 = -2x + x3 + -1x3
2 + -6x + 2x2 = -2x + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
2 + -6x + 2x2 = -2x + 0
2 + -6x + 2x2 = -2x

Solving
2 + -6x + 2x2 = -2x

Solving for variable 'x'.

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

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

Combine like terms: -2x + 2x = 0
2 + -4x + 2x2 = 0

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

Factor a trinomial.
2((1 + -1x)(1 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {1, 1}

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