(9x^3-7x^2+5x)+(6x^3+9x^2-12x)=

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Solution for (9x^3-7x^2+5x)+(6x^3+9x^2-12x)= equation: 


Simplifying
(9x3 + -7x2 + 5x) + (6x3 + 9x2 + -12x) = 0

Reorder the terms:
(5x + -7x2 + 9x3) + (6x3 + 9x2 + -12x) = 0

Remove parenthesis around (5x + -7x2 + 9x3)
5x + -7x2 + 9x3 + (6x3 + 9x2 + -12x) = 0

Reorder the terms:
5x + -7x2 + 9x3 + (-12x + 9x2 + 6x3) = 0

Remove parenthesis around (-12x + 9x2 + 6x3)
5x + -7x2 + 9x3 + -12x + 9x2 + 6x3 = 0

Reorder the terms:
5x + -12x + -7x2 + 9x2 + 9x3 + 6x3 = 0

Combine like terms: 5x + -12x = -7x
-7x + -7x2 + 9x2 + 9x3 + 6x3 = 0

Combine like terms: -7x2 + 9x2 = 2x2
-7x + 2x2 + 9x3 + 6x3 = 0

Combine like terms: 9x3 + 6x3 = 15x3
-7x + 2x2 + 15x3 = 0

Solving
-7x + 2x2 + 15x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-7 + 2x + 15x2) = 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 '(-7 + 2x + 15x2)' equal to zero and attempt to solve:

Simplifying
-7 + 2x + 15x2 = 0

Solving
-7 + 2x + 15x2 = 0

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

Divide each side by '15'.
-0.4666666667 + 0.1333333333x + x2 = 0

Move the constant term to the right:

Add '0.4666666667' to each side of the equation.
-0.4666666667 + 0.1333333333x + 0.4666666667 + x2 = 0 + 0.4666666667

Reorder the terms:
-0.4666666667 + 0.4666666667 + 0.1333333333x + x2 = 0 + 0.4666666667

Combine like terms: -0.4666666667 + 0.4666666667 = 0.0000000000
0.0000000000 + 0.1333333333x + x2 = 0 + 0.4666666667
0.1333333333x + x2 = 0 + 0.4666666667

Combine like terms: 0 + 0.4666666667 = 0.4666666667
0.1333333333x + x2 = 0.4666666667

The x term is 0.1333333333x.  Take half its coefficient (0.06666666665).
Square it (0.004444444442) and add it to both sides.

Add '0.004444444442' to each side of the equation.
0.1333333333x + 0.004444444442 + x2 = 0.4666666667 + 0.004444444442

Reorder the terms:
0.004444444442 + 0.1333333333x + x2 = 0.4666666667 + 0.004444444442

Combine like terms: 0.4666666667 + 0.004444444442 = 0.471111111142
0.004444444442 + 0.1333333333x + x2 = 0.471111111142

Factor a perfect square on the left side:
(x + 0.06666666665)(x + 0.06666666665) = 0.471111111142

Calculate the square root of the right side: 0.686375343

Break this problem into two subproblems by setting 
(x + 0.06666666665) equal to 0.686375343 and -0.686375343.


Subproblem 1
x + 0.06666666665 = 0.686375343

Simplifying
x + 0.06666666665 = 0.686375343

Reorder the terms:
0.06666666665 + x = 0.686375343

Solving
0.06666666665 + x = 0.686375343

Solving for variable 'x'.

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

Add '-0.06666666665' to each side of the equation.
0.06666666665 + -0.06666666665 + x = 0.686375343 + -0.06666666665

Combine like terms: 0.06666666665 + -0.06666666665 = 0.00000000000
0.00000000000 + x = 0.686375343 + -0.06666666665
x = 0.686375343 + -0.06666666665

Combine like terms: 0.686375343 + -0.06666666665 = 0.61970867635
x = 0.61970867635

Simplifying
x = 0.61970867635


Subproblem 2
x + 0.06666666665 = -0.686375343

Simplifying
x + 0.06666666665 = -0.686375343

Reorder the terms:
0.06666666665 + x = -0.686375343

Solving
0.06666666665 + x = -0.686375343

Solving for variable 'x'.

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

Add '-0.06666666665' to each side of the equation.
0.06666666665 + -0.06666666665 + x = -0.686375343 + -0.06666666665

Combine like terms: 0.06666666665 + -0.06666666665 = 0.00000000000
0.00000000000 + x = -0.686375343 + -0.06666666665
x = -0.686375343 + -0.06666666665

Combine like terms: -0.686375343 + -0.06666666665 = -0.75304200965
x = -0.75304200965

Simplifying
x = -0.75304200965


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.61970867635, -0.75304200965}
Solution
x = {0, 0.61970867635, -0.75304200965}

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