-3x^3(2x^2+4x-9)=0

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Solution for -3x^3(2x^2+4x-9)=0 equation: 


Simplifying
-3x3(2x2 + 4x + -9) = 0

Reorder the terms:
-3x3(-9 + 4x + 2x2) = 0
(-9 * -3x3 + 4x * -3x3 + 2x2 * -3x3) = 0
(27x3 + -12x4 + -6x5) = 0

Solving
27x3 + -12x4 + -6x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x3'.
3x3(9 + -4x + -2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(9 + -4x + -2x2)' equal to zero and attempt to solve:

Simplifying
9 + -4x + -2x2 = 0

Solving
9 + -4x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-4.5 + 2x + x2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + 2x + 4.5 + x2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + 2x + x2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + 2x + x2 = 0 + 4.5
2x + x2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
2x + x2 = 4.5

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 4.5 + 1

Reorder the terms:
1 + 2x + x2 = 4.5 + 1

Combine like terms: 4.5 + 1 = 5.5
1 + 2x + x2 = 5.5

Factor a perfect square on the left side:
(x + 1)(x + 1) = 5.5

Calculate the square root of the right side: 2.34520788

Break this problem into two subproblems by setting 
(x + 1) equal to 2.34520788 and -2.34520788.


Subproblem 1
x + 1 = 2.34520788

Simplifying
x + 1 = 2.34520788

Reorder the terms:
1 + x = 2.34520788

Solving
1 + x = 2.34520788

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + x = 2.34520788 + -1

Combine like terms: 1 + -1 = 0
0 + x = 2.34520788 + -1
x = 2.34520788 + -1

Combine like terms: 2.34520788 + -1 = 1.34520788
x = 1.34520788

Simplifying
x = 1.34520788


Subproblem 2
x + 1 = -2.34520788

Simplifying
x + 1 = -2.34520788

Reorder the terms:
1 + x = -2.34520788

Solving
1 + x = -2.34520788

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + x = -2.34520788 + -1

Combine like terms: 1 + -1 = 0
0 + x = -2.34520788 + -1
x = -2.34520788 + -1

Combine like terms: -2.34520788 + -1 = -3.34520788
x = -3.34520788

Simplifying
x = -3.34520788


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.34520788, -3.34520788}
Solution
x = {1.34520788, -3.34520788}

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