45x^3+36x^2+9x=0

Solution for 45x^3+36x^2+9x=0 equation:

Simplifying
45x3 + 36x2 + 9x = 0

Reorder the terms:
9x + 36x2 + 45x3 = 0

Solving
9x + 36x2 + 45x3 = 0

Solving for variable 'x'.

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

Ignore the factor 9.
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 '(1 + 4x + 5x2)' equal to zero and attempt to solve:

Simplifying
1 + 4x + 5x2 = 0

Solving
1 + 4x + 5x2 = 0

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

Divide each side by '5'.
0.2 + 0.8x + x2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 0.8x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 0.8x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 0.8x + x2 = 0 + -0.2
0.8x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
0.8x + x2 = -0.2

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = -0.2 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = -0.2 + 0.16

Combine like terms: -0.2 + 0.16 = -0.04
0.16 + 0.8x + x2 = -0.04

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = -0.04

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}