0=x^3-8x^2+18x

Solution for 0=x^3-8x^2+18x equation:

Simplifying
0 = x3 + -8x2 + 18x

Reorder the terms:
0 = 18x + -8x2 + x3

Solving
0 = 18x + -8x2 + x3

Solving for variable 'x'.
Remove the zero:
-18x + 8x2 + -1x3 = 18x + -8x2 + x3 + -18x + 8x2 + -1x3

Reorder the terms:
-18x + 8x2 + -1x3 = 18x + -18x + -8x2 + 8x2 + x3 + -1x3

Combine like terms: 18x + -18x = 0
-18x + 8x2 + -1x3 = 0 + -8x2 + 8x2 + x3 + -1x3
-18x + 8x2 + -1x3 = -8x2 + 8x2 + x3 + -1x3

Combine like terms: -8x2 + 8x2 = 0
-18x + 8x2 + -1x3 = 0 + x3 + -1x3
-18x + 8x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-18x + 8x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-18 + 8x + -1x2) = 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 '(-18 + 8x + -1x2)' equal to zero and attempt to solve:

Simplifying
-18 + 8x + -1x2 = 0

Solving
-18 + 8x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
18 + -8x + x2 = 0

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -8x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + -8x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -8x + x2 = 0 + -18
-8x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
-8x + x2 = -18

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 = -18 + 16

Reorder the terms:
16 + -8x + x2 = -18 + 16

Combine like terms: -18 + 16 = -2
16 + -8x + x2 = -2

Factor a perfect square on the left side:
(x + -4)(x + -4) = -2

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}