3x^3-10x^2+24x=0

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Solution for 3x^3-10x^2+24x=0 equation: 


Simplifying
3x3 + -10x2 + 24x = 0

Reorder the terms:
24x + -10x2 + 3x3 = 0

Solving
24x + -10x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(24 + -10x + 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 '(24 + -10x + 3x2)' equal to zero and attempt to solve:

Simplifying
24 + -10x + 3x2 = 0

Solving
24 + -10x + 3x2 = 0

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

Divide each side by '3'.
8 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -3.333333333x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -3.333333333x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3.333333333x + x2 = 0 + -8
-3.333333333x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-3.333333333x + x2 = -8

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = -8 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = -8 + 2.777777779

Combine like terms: -8 + 2.777777779 = -5.222222221
2.777777779 + -3.333333333x + x2 = -5.222222221

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = -5.222222221

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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