(x^5)-(14x^4)+(4x^3)=0

Solution for (x^5)-(14x^4)+(4x^3)=0 equation:

Simplifying
(x5) + -1(14x4) + (4x3) = 0
x5 + -1(14x4) + (4x3) = 0

Remove parenthesis around (14x4)
x5 + -1 * 14x4 + (4x3) = 0

Multiply -1 * 14
x5 + -14x4 + (4x3) = 0

Reorder the terms:
(4x3) + -14x4 + x5 = 0

Solving
(4x3) + -14x4 + x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x3'.
x3(4 + -14x + 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 '(4 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
4 + -14x + x2 = 0

Solving
4 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -14x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -14x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -14x + x2 = 0 + -4
-14x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-14x + x2 = -4

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -4 + 49

Reorder the terms:
49 + -14x + x2 = -4 + 49

Combine like terms: -4 + 49 = 45
49 + -14x + x2 = 45

Factor a perfect square on the left side:
(x + -7)(x + -7) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(x + -7) equal to 6.708203933 and -6.708203933.

Subproblem 1
x + -7 = 6.708203933

Simplifying
x + -7 = 6.708203933

Reorder the terms:
-7 + x = 6.708203933

Solving
-7 + x = 6.708203933

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 6.708203933 + 7

Combine like terms: -7 + 7 = 0
0 + x = 6.708203933 + 7
x = 6.708203933 + 7

Combine like terms: 6.708203933 + 7 = 13.708203933
x = 13.708203933

Simplifying
x = 13.708203933

Subproblem 2
x + -7 = -6.708203933

Simplifying
x + -7 = -6.708203933

Reorder the terms:
-7 + x = -6.708203933

Solving
-7 + x = -6.708203933

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -6.708203933 + 7

Combine like terms: -7 + 7 = 0
0 + x = -6.708203933 + 7
x = -6.708203933 + 7

Combine like terms: -6.708203933 + 7 = 0.291796067
x = 0.291796067

Simplifying
x = 0.291796067

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.708203933, 0.291796067}
Solution
x = {13.708203933, 0.291796067}