9x^5-12x^3-15x=

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Solution for 9x^5-12x^3-15x= equation: 


Simplifying
9x5 + -12x3 + -15x = 0

Reorder the terms:
-15x + -12x3 + 9x5 = 0

Solving
-15x + -12x3 + 9x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-5 + -4x2 + 3x4) = 0

Ignore the factor 3.

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 '(-5 + -4x2 + 3x4)' equal to zero and attempt to solve:

Simplifying
-5 + -4x2 + 3x4 = 0

Solving
-5 + -4x2 + 3x4 = 0

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

Divide each side by '3'.
-1.666666667 + -1.333333333x2 + x4 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -1.333333333x2 + 1.666666667 + x4 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -1.333333333x2 + x4 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -1.333333333x2 + x4 = 0 + 1.666666667
-1.333333333x2 + x4 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-1.333333333x2 + x4 = 1.666666667

The x term is -1.333333333x2.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x2 + 0.4444444442 + x4 = 1.666666667 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x2 + x4 = 1.666666667 + 0.4444444442

Combine like terms: 1.666666667 + 0.4444444442 = 2.1111111112
0.4444444442 + -1.333333333x2 + x4 = 2.1111111112

Factor a perfect square on the left side:
(x2 + -0.6666666665)(x2 + -0.6666666665) = 2.1111111112

Calculate the square root of the right side: 1.452966315

Break this problem into two subproblems by setting 
(x2 + -0.6666666665) equal to 1.452966315 and -1.452966315.


Subproblem 1
x2 + -0.6666666665 = 1.452966315

Simplifying
x2 + -0.6666666665 = 1.452966315

Reorder the terms:
-0.6666666665 + x2 = 1.452966315

Solving
-0.6666666665 + x2 = 1.452966315

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x2 = 1.452966315 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x2 = 1.452966315 + 0.6666666665
x2 = 1.452966315 + 0.6666666665

Combine like terms: 1.452966315 + 0.6666666665 = 2.1196329815
x2 = 2.1196329815

Simplifying
x2 = 2.1196329815

Take the square root of each side:
x = {-1.455895938, 1.455895938}


Subproblem 2
x2 + -0.6666666665 = -1.452966315

Simplifying
x2 + -0.6666666665 = -1.452966315

Reorder the terms:
-0.6666666665 + x2 = -1.452966315

Solving
-0.6666666665 + x2 = -1.452966315

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x2 = -1.452966315 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x2 = -1.452966315 + 0.6666666665
x2 = -1.452966315 + 0.6666666665

Combine like terms: -1.452966315 + 0.6666666665 = -0.7862996485
x2 = -0.7862996485

Simplifying
x2 = -0.7862996485

Reorder the terms:
0.7862996485 + x2 = -0.7862996485 + 0.7862996485

Combine like terms: -0.7862996485 + 0.7862996485 = 0.0000000000
0.7862996485 + x2 = 0.0000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

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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