x^3+x^2+x+6=3x^2+6

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Solution for x^3+x^2+x+6=3x^2+6 equation: 


Simplifying
x3 + x2 + x + 6 = 3x2 + 6

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

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

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

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

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

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

Solving
x + x2 + x3 = 3x2

Solving for variable 'x'.

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

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

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

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

Factor a trinomial.
x((1 + -1x)(1 + -1x)) = 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 '(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 3
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 = {0, 1, 1}

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