x^3-2x^2-2x+7=6x+7

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Solution for x^3-2x^2-2x+7=6x+7 equation: 


Simplifying
x3 + -2x2 + -2x + 7 = 6x + 7

Reorder the terms:
7 + -2x + -2x2 + x3 = 6x + 7

Reorder the terms:
7 + -2x + -2x2 + x3 = 7 + 6x

Add '-7' to each side of the equation.
7 + -2x + -2x2 + -7 + x3 = 7 + -7 + 6x

Reorder the terms:
7 + -7 + -2x + -2x2 + x3 = 7 + -7 + 6x

Combine like terms: 7 + -7 = 0
0 + -2x + -2x2 + x3 = 7 + -7 + 6x
-2x + -2x2 + x3 = 7 + -7 + 6x

Combine like terms: 7 + -7 = 0
-2x + -2x2 + x3 = 0 + 6x
-2x + -2x2 + x3 = 6x

Solving
-2x + -2x2 + x3 = 6x

Solving for variable 'x'.

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

Combine like terms: -2x + -6x = -8x
-8x + -2x2 + x3 = 6x + -6x

Combine like terms: 6x + -6x = 0
-8x + -2x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-8 + -2x + x2) = 0

Factor a trinomial.
x((-2 + -1x)(4 + -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 '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0, -2, 4}

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