8x^3-16x^2+36x=0

Solution for 8x^3-16x^2+36x=0 equation:

Simplifying
8x3 + -16x2 + 36x = 0

Reorder the terms:
36x + -16x2 + 8x3 = 0

Solving
36x + -16x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(9 + -4x + 2x2) = 0

Ignore the factor 4.
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 '(9 + -4x + 2x2)' equal to zero and attempt to solve:

Simplifying
9 + -4x + 2x2 = 0

Solving
9 + -4x + 2x2 = 0

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

Divide each side by '2'.
4.5 + -2x + x2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + -2x + -4.5 + x2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + -2x + x2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + -2x + x2 = 0 + -4.5
-2x + x2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
-2x + x2 = -4.5

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -4.5 + 1

Reorder the terms:
1 + -2x + x2 = -4.5 + 1

Combine like terms: -4.5 + 1 = -3.5
1 + -2x + x2 = -3.5

Factor a perfect square on the left side:
(x + -1)(x + -1) = -3.5

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}