3x^5-24x^4+18x^3=0

Solution for 3x^5-24x^4+18x^3=0 equation:

Simplifying
3x5 + -24x4 + 18x3 = 0

Reorder the terms:
18x3 + -24x4 + 3x5 = 0

Solving
18x3 + -24x4 + 3x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x3'.
3x3(6 + -8x + x2) = 0

Ignore the factor 3.
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 '(6 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
6 + -8x + x2 = 0

Solving
6 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -8x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -8x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -8x + x2 = 0 + -6
-8x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-8x + x2 = -6

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -6 + 16

Reorder the terms:
16 + -8x + x2 = -6 + 16

Combine like terms: -6 + 16 = 10
16 + -8x + x2 = 10

Factor a perfect square on the left side:
(x + -4)(x + -4) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + -4) equal to 3.16227766 and -3.16227766.

Subproblem 1
x + -4 = 3.16227766

Simplifying
x + -4 = 3.16227766

Reorder the terms:
-4 + x = 3.16227766

Solving
-4 + x = 3.16227766

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 3.16227766 + 4

Combine like terms: -4 + 4 = 0
0 + x = 3.16227766 + 4
x = 3.16227766 + 4

Combine like terms: 3.16227766 + 4 = 7.16227766
x = 7.16227766

Simplifying
x = 7.16227766

Subproblem 2
x + -4 = -3.16227766

Simplifying
x + -4 = -3.16227766

Reorder the terms:
-4 + x = -3.16227766

Solving
-4 + x = -3.16227766

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -3.16227766 + 4

Combine like terms: -4 + 4 = 0
0 + x = -3.16227766 + 4
x = -3.16227766 + 4

Combine like terms: -3.16227766 + 4 = 0.83772234
x = 0.83772234

Simplifying
x = 0.83772234

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.16227766, 0.83772234}
Solution
x = {7.16227766, 0.83772234}