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

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


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

Reorder the terms:
-2 + -6x + x3 = 3x2 + -2(3x + 1)

Reorder the terms:
-2 + -6x + x3 = 3x2 + -2(1 + 3x)
-2 + -6x + x3 = 3x2 + (1 * -2 + 3x * -2)
-2 + -6x + x3 = 3x2 + (-2 + -6x)

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

Add '2' to each side of the equation.
-2 + -6x + 2 + x3 = -2 + -6x + 2 + 3x2

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

Combine like terms: -2 + 2 = 0
0 + -6x + x3 = -2 + -6x + 2 + 3x2
-6x + x3 = -2 + -6x + 2 + 3x2

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

Combine like terms: -2 + 2 = 0
-6x + x3 = 0 + -6x + 3x2
-6x + x3 = -6x + 3x2

Add '6x' to each side of the equation.
-6x + 6x + x3 = -6x + 6x + 3x2

Combine like terms: -6x + 6x = 0
0 + x3 = -6x + 6x + 3x2
x3 = -6x + 6x + 3x2

Combine like terms: -6x + 6x = 0
x3 = 0 + 3x2
x3 = 3x2

Solving
x3 = 3x2

Solving for variable 'x'.

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

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

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-3 + x) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

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

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

Combine like terms: 0 + 3 = 3
x = 3

Simplifying
x = 3
Solution
x = {0, 3}

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