x(3x^2-2x+21)=0

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Solution for x(3x^2-2x+21)=0 equation: 


Simplifying
x(3x2 + -2x + 21) = 0

Reorder the terms:
x(21 + -2x + 3x2) = 0
(21 * x + -2x * x + 3x2 * x) = 0
(21x + -2x2 + 3x3) = 0

Solving
21x + -2x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(21 + -2x + 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 '(21 + -2x + 3x2)' equal to zero and attempt to solve:

Simplifying
21 + -2x + 3x2 = 0

Solving
21 + -2x + 3x2 = 0

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

Divide each side by '3'.
7 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -0.6666666667x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + -0.6666666667x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -0.6666666667x + x2 = 0 + -7
-0.6666666667x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-0.6666666667x + x2 = -7

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = -7 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = -7 + 0.1111111112

Combine like terms: -7 + 0.1111111112 = -6.8888888888
0.1111111112 + -0.6666666667x + x2 = -6.8888888888

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = -6.8888888888

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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