9x^3-9x^2+20x=0

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Solution for 9x^3-9x^2+20x=0 equation: 


Simplifying
9x3 + -9x2 + 20x = 0

Reorder the terms:
20x + -9x2 + 9x3 = 0

Solving
20x + -9x2 + 9x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(20 + -9x + 9x2) = 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 '(20 + -9x + 9x2)' equal to zero and attempt to solve:

Simplifying
20 + -9x + 9x2 = 0

Solving
20 + -9x + 9x2 = 0

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

Divide each side by '9'.
2.222222222 + -1x + x2 = 0

Move the constant term to the right:

Add '-2.222222222' to each side of the equation.
2.222222222 + -1x + -2.222222222 + x2 = 0 + -2.222222222

Reorder the terms:
2.222222222 + -2.222222222 + -1x + x2 = 0 + -2.222222222

Combine like terms: 2.222222222 + -2.222222222 = 0.000000000
0.000000000 + -1x + x2 = 0 + -2.222222222
-1x + x2 = 0 + -2.222222222

Combine like terms: 0 + -2.222222222 = -2.222222222
-1x + x2 = -2.222222222

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -2.222222222 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -2.222222222 + 0.25

Combine like terms: -2.222222222 + 0.25 = -1.972222222
0.25 + -1x + x2 = -1.972222222

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -1.972222222

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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