9x^3+21x^2+20x=0

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Solution for 9x^3+21x^2+20x=0 equation: 


Simplifying
9x3 + 21x2 + 20x = 0

Reorder the terms:
20x + 21x2 + 9x3 = 0

Solving
20x + 21x2 + 9x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(20 + 21x + 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 + 21x + 9x2)' equal to zero and attempt to solve:

Simplifying
20 + 21x + 9x2 = 0

Solving
20 + 21x + 9x2 = 0

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

Divide each side by '9'.
2.222222222 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '-2.222222222' to each side of the equation.
2.222222222 + 2.333333333x + -2.222222222 + x2 = 0 + -2.222222222

Reorder the terms:
2.222222222 + -2.222222222 + 2.333333333x + x2 = 0 + -2.222222222

Combine like terms: 2.222222222 + -2.222222222 = 0.000000000
0.000000000 + 2.333333333x + x2 = 0 + -2.222222222
2.333333333x + x2 = 0 + -2.222222222

Combine like terms: 0 + -2.222222222 = -2.222222222
2.333333333x + x2 = -2.222222222

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 = -2.222222222 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = -2.222222222 + 1.361111112

Combine like terms: -2.222222222 + 1.361111112 = -0.86111111
1.361111112 + 2.333333333x + x2 = -0.86111111

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = -0.86111111

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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