9x^3-7x^2+4x^2-x+4x^3-3x^2=

Solution for 9x^3-7x^2+4x^2-x+4x^3-3x^2= equation:

Simplifying
9x3 + -7x2 + 4x2 + -1x + 4x3 + -3x2 = 0

Reorder the terms:
-1x + -7x2 + 4x2 + -3x2 + 9x3 + 4x3 = 0

Combine like terms: -7x2 + 4x2 = -3x2
-1x + -3x2 + -3x2 + 9x3 + 4x3 = 0

Combine like terms: -3x2 + -3x2 = -6x2
-1x + -6x2 + 9x3 + 4x3 = 0

Combine like terms: 9x3 + 4x3 = 13x3
-1x + -6x2 + 13x3 = 0

Solving
-1x + -6x2 + 13x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + -6x + 13x2) = 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 + 13x2)' equal to zero and attempt to solve:

Simplifying
-1 + -6x + 13x2 = 0

Solving
-1 + -6x + 13x2 = 0

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

Divide each side by '13'.
-0.07692307692 + -0.4615384615x + x2 = 0

Move the constant term to the right:

Add '0.07692307692' to each side of the equation.
-0.07692307692 + -0.4615384615x + 0.07692307692 + x2 = 0 + 0.07692307692

Reorder the terms:
-0.07692307692 + 0.07692307692 + -0.4615384615x + x2 = 0 + 0.07692307692

Combine like terms: -0.07692307692 + 0.07692307692 = 0.00000000000
0.00000000000 + -0.4615384615x + x2 = 0 + 0.07692307692
-0.4615384615x + x2 = 0 + 0.07692307692

Combine like terms: 0 + 0.07692307692 = 0.07692307692
-0.4615384615x + x2 = 0.07692307692

The x term is -0.4615384615x.  Take half its coefficient (-0.2307692308).
Square it (0.05325443788) and add it to both sides.

Add '0.05325443788' to each side of the equation.
-0.4615384615x + 0.05325443788 + x2 = 0.07692307692 + 0.05325443788

Reorder the terms:
0.05325443788 + -0.4615384615x + x2 = 0.07692307692 + 0.05325443788

Combine like terms: 0.07692307692 + 0.05325443788 = 0.1301775148
0.05325443788 + -0.4615384615x + x2 = 0.1301775148

Factor a perfect square on the left side:
(x + -0.2307692308)(x + -0.2307692308) = 0.1301775148

Calculate the square root of the right side: 0.360801212

Break this problem into two subproblems by setting 
(x + -0.2307692308) equal to 0.360801212 and -0.360801212.

Subproblem 1
x + -0.2307692308 = 0.360801212

Simplifying
x + -0.2307692308 = 0.360801212

Reorder the terms:
-0.2307692308 + x = 0.360801212

Solving
-0.2307692308 + x = 0.360801212

Solving for variable 'x'.

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

Add '0.2307692308' to each side of the equation.
-0.2307692308 + 0.2307692308 + x = 0.360801212 + 0.2307692308

Combine like terms: -0.2307692308 + 0.2307692308 = 0.0000000000
0.0000000000 + x = 0.360801212 + 0.2307692308
x = 0.360801212 + 0.2307692308

Combine like terms: 0.360801212 + 0.2307692308 = 0.5915704428
x = 0.5915704428

Simplifying
x = 0.5915704428

Subproblem 2
x + -0.2307692308 = -0.360801212

Simplifying
x + -0.2307692308 = -0.360801212

Reorder the terms:
-0.2307692308 + x = -0.360801212

Solving
-0.2307692308 + x = -0.360801212

Solving for variable 'x'.

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

Add '0.2307692308' to each side of the equation.
-0.2307692308 + 0.2307692308 + x = -0.360801212 + 0.2307692308

Combine like terms: -0.2307692308 + 0.2307692308 = 0.0000000000
0.0000000000 + x = -0.360801212 + 0.2307692308
x = -0.360801212 + 0.2307692308

Combine like terms: -0.360801212 + 0.2307692308 = -0.1300319812
x = -0.1300319812

Simplifying
x = -0.1300319812

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5915704428, -0.1300319812}
Solution
x = {0, 0.5915704428, -0.1300319812}