9x^3+2x^2+5x^3+4x^2=x

Solution for 9x^3+2x^2+5x^3+4x^2=x equation:

Simplifying
9x3 + 2x2 + 5x3 + 4x2 = x

Reorder the terms:
2x2 + 4x2 + 9x3 + 5x3 = x

Combine like terms: 2x2 + 4x2 = 6x2
6x2 + 9x3 + 5x3 = x

Combine like terms: 9x3 + 5x3 = 14x3
6x2 + 14x3 = x

Solving
6x2 + 14x3 = x

Solving for variable 'x'.

Reorder the terms:
-1x + 6x2 + 14x3 = x + -1x

Combine like terms: x + -1x = 0
-1x + 6x2 + 14x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + 6x + 14x2) = 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 '(-1 + 6x + 14x2)' equal to zero and attempt to solve:

Simplifying
-1 + 6x + 14x2 = 0

Solving
-1 + 6x + 14x2 = 0

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

Divide each side by '14'.
-0.07142857143 + 0.4285714286x + x2 = 0

Move the constant term to the right:

Add '0.07142857143' to each side of the equation.
-0.07142857143 + 0.4285714286x + 0.07142857143 + x2 = 0 + 0.07142857143

Reorder the terms:
-0.07142857143 + 0.07142857143 + 0.4285714286x + x2 = 0 + 0.07142857143

Combine like terms: -0.07142857143 + 0.07142857143 = 0.00000000000
0.00000000000 + 0.4285714286x + x2 = 0 + 0.07142857143
0.4285714286x + x2 = 0 + 0.07142857143

Combine like terms: 0 + 0.07142857143 = 0.07142857143
0.4285714286x + x2 = 0.07142857143

The x term is 0.4285714286x.  Take half its coefficient (0.2142857143).
Square it (0.04591836735) and add it to both sides.

Add '0.04591836735' to each side of the equation.
0.4285714286x + 0.04591836735 + x2 = 0.07142857143 + 0.04591836735

Reorder the terms:
0.04591836735 + 0.4285714286x + x2 = 0.07142857143 + 0.04591836735

Combine like terms: 0.07142857143 + 0.04591836735 = 0.11734693878
0.04591836735 + 0.4285714286x + x2 = 0.11734693878

Factor a perfect square on the left side:
(x + 0.2142857143)(x + 0.2142857143) = 0.11734693878

Calculate the square root of the right side: 0.342559395

Break this problem into two subproblems by setting 
(x + 0.2142857143) equal to 0.342559395 and -0.342559395.

Subproblem 1
x + 0.2142857143 = 0.342559395

Simplifying
x + 0.2142857143 = 0.342559395

Reorder the terms:
0.2142857143 + x = 0.342559395

Solving
0.2142857143 + x = 0.342559395

Solving for variable 'x'.

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

Add '-0.2142857143' to each side of the equation.
0.2142857143 + -0.2142857143 + x = 0.342559395 + -0.2142857143

Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000
0.0000000000 + x = 0.342559395 + -0.2142857143
x = 0.342559395 + -0.2142857143

Combine like terms: 0.342559395 + -0.2142857143 = 0.1282736807
x = 0.1282736807

Simplifying
x = 0.1282736807

Subproblem 2
x + 0.2142857143 = -0.342559395

Simplifying
x + 0.2142857143 = -0.342559395

Reorder the terms:
0.2142857143 + x = -0.342559395

Solving
0.2142857143 + x = -0.342559395

Solving for variable 'x'.

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

Add '-0.2142857143' to each side of the equation.
0.2142857143 + -0.2142857143 + x = -0.342559395 + -0.2142857143

Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000
0.0000000000 + x = -0.342559395 + -0.2142857143
x = -0.342559395 + -0.2142857143

Combine like terms: -0.342559395 + -0.2142857143 = -0.5568451093
x = -0.5568451093

Simplifying
x = -0.5568451093

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.1282736807, -0.5568451093}
Solution
x = {0, 0.1282736807, -0.5568451093}