8x(2x^2-3x+3)=0

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

Simplifying
8x(2x2 + -3x + 3) = 0

Reorder the terms:
8x(3 + -3x + 2x2) = 0
(3 * 8x + -3x * 8x + 2x2 * 8x) = 0
(24x + -24x2 + 16x3) = 0

Solving
24x + -24x2 + 16x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8x'.
8x(3 + -3x + 2x2) = 0

Ignore the factor 8.
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 '(3 + -3x + 2x2)' equal to zero and attempt to solve:

Simplifying
3 + -3x + 2x2 = 0

Solving
3 + -3x + 2x2 = 0

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

Divide each side by '2'.
1.5 + -1.5x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -1.5x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -1.5x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -1.5x + x2 = 0 + -1.5
-1.5x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-1.5x + x2 = -1.5

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = -1.5 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = -1.5 + 0.5625

Combine like terms: -1.5 + 0.5625 = -0.9375
0.5625 + -1.5x + x2 = -0.9375

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = -0.9375

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}