3x^3-7x^2-6x+14x=0

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Solution for 3x^3-7x^2-6x+14x=0 equation: 


Simplifying
3x3 + -7x2 + -6x + 14x = 0

Reorder the terms:
-6x + 14x + -7x2 + 3x3 = 0

Combine like terms: -6x + 14x = 8x
8x + -7x2 + 3x3 = 0

Solving
8x + -7x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(8 + -7x + 3x2) = 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 '(8 + -7x + 3x2)' equal to zero and attempt to solve:

Simplifying
8 + -7x + 3x2 = 0

Solving
8 + -7x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
2.666666667 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.333333333x + -2.666666667 + x2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + -2.333333333x + x2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + -2.333333333x + x2 = 0 + -2.666666667
-2.333333333x + x2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
-2.333333333x + x2 = -2.666666667

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = -2.666666667 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = -2.666666667 + 1.361111112

Combine like terms: -2.666666667 + 1.361111112 = -1.305555555
1.361111112 + -2.333333333x + x2 = -1.305555555

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = -1.305555555

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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