20x^3-5x^2+45x=0

Solution for 20x^3-5x^2+45x=0 equation:

Simplifying
20x3 + -5x2 + 45x = 0

Reorder the terms:
45x + -5x2 + 20x3 = 0

Solving
45x + -5x2 + 20x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(9 + -1x + 4x2) = 0

Ignore the factor 5.
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 + -1x + 4x2)' equal to zero and attempt to solve:

Simplifying
9 + -1x + 4x2 = 0

Solving
9 + -1x + 4x2 = 0

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

Divide each side by '4'.
2.25 + -0.25x + x2 = 0

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + -0.25x + -2.25 + x2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + -0.25x + x2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + -0.25x + x2 = 0 + -2.25
-0.25x + x2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
-0.25x + x2 = -2.25

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = -2.25 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = -2.25 + 0.015625

Combine like terms: -2.25 + 0.015625 = -2.234375
0.015625 + -0.25x + x2 = -2.234375

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = -2.234375

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}