x^2-9x^3=20x

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

Simplifying
x2 + -9x3 = 20x

Solving
x2 + -9x3 = 20x

Solving for variable 'x'.

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

Combine like terms: 20x + -20x = 0
-20x + x2 + -9x3 = 0

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

Simplifying
-20 + x + -9x2 = 0

Solving
-20 + x + -9x2 = 0

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

Divide each side by '-9'.
2.222222222 + -0.1111111111x + x2 = 0

Move the constant term to the right:

Add '-2.222222222' to each side of the equation.
2.222222222 + -0.1111111111x + -2.222222222 + x2 = 0 + -2.222222222

Reorder the terms:
2.222222222 + -2.222222222 + -0.1111111111x + x2 = 0 + -2.222222222

Combine like terms: 2.222222222 + -2.222222222 = 0.000000000
0.000000000 + -0.1111111111x + x2 = 0 + -2.222222222
-0.1111111111x + x2 = 0 + -2.222222222

Combine like terms: 0 + -2.222222222 = -2.222222222
-0.1111111111x + x2 = -2.222222222

The x term is x.  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.
-0.1111111111x + 0.25 + x2 = -2.222222222 + 0.25

Reorder the terms:
0.25 + -0.1111111111x + x2 = -2.222222222 + 0.25

Combine like terms: -2.222222222 + 0.25 = -1.972222222
0.25 + -0.1111111111x + 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}