x^5-6x^4-3x^3=

Solution for x^5-6x^4-3x^3= equation:

Simplifying
x5 + -6x4 + -3x3 = 0

Reorder the terms:
-3x3 + -6x4 + x5 = 0

Solving
-3x3 + -6x4 + x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x3'.
x3(-3 + -6x + x2) = 0

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 '(-3 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
-3 + -6x + x2 = 0

Solving
-3 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -6x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -6x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -6x + x2 = 0 + 3
-6x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-6x + x2 = 3

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 3 + 9

Reorder the terms:
9 + -6x + x2 = 3 + 9

Combine like terms: 3 + 9 = 12
9 + -6x + x2 = 12

Factor a perfect square on the left side:
(x + -3)(x + -3) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + -3) equal to 3.464101615 and -3.464101615.

Subproblem 1
x + -3 = 3.464101615

Simplifying
x + -3 = 3.464101615

Reorder the terms:
-3 + x = 3.464101615

Solving
-3 + x = 3.464101615

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 3.464101615 + 3

Combine like terms: -3 + 3 = 0
0 + x = 3.464101615 + 3
x = 3.464101615 + 3

Combine like terms: 3.464101615 + 3 = 6.464101615
x = 6.464101615

Simplifying
x = 6.464101615

Subproblem 2
x + -3 = -3.464101615

Simplifying
x + -3 = -3.464101615

Reorder the terms:
-3 + x = -3.464101615

Solving
-3 + x = -3.464101615

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -3.464101615 + 3

Combine like terms: -3 + 3 = 0
0 + x = -3.464101615 + 3
x = -3.464101615 + 3

Combine like terms: -3.464101615 + 3 = -0.464101615
x = -0.464101615

Simplifying
x = -0.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.464101615, -0.464101615}
Solution
x = {6.464101615, -0.464101615}