10r^3+45r^2+405r=0

Solution for 10r^3+45r^2+405r=0 equation:

Simplifying
10r3 + 45r2 + 405r = 0

Reorder the terms:
405r + 45r2 + 10r3 = 0

Solving
405r + 45r2 + 10r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '5r'.
5r(81 + 9r + 2r2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

Move all terms containing r to the left, all other terms to the right.

Simplifying
r = 0
Subproblem 2
Set the factor '(81 + 9r + 2r2)' equal to zero and attempt to solve:

Simplifying
81 + 9r + 2r2 = 0

Solving
81 + 9r + 2r2 = 0

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

Divide each side by '2'.
40.5 + 4.5r + r2 = 0

Move the constant term to the right:

Add '-40.5' to each side of the equation.
40.5 + 4.5r + -40.5 + r2 = 0 + -40.5

Reorder the terms:
40.5 + -40.5 + 4.5r + r2 = 0 + -40.5

Combine like terms: 40.5 + -40.5 = 0.0
0.0 + 4.5r + r2 = 0 + -40.5
4.5r + r2 = 0 + -40.5

Combine like terms: 0 + -40.5 = -40.5
4.5r + r2 = -40.5

The r term is 4.5r.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5r + 5.0625 + r2 = -40.5 + 5.0625

Reorder the terms:
5.0625 + 4.5r + r2 = -40.5 + 5.0625

Combine like terms: -40.5 + 5.0625 = -35.4375
5.0625 + 4.5r + r2 = -35.4375

Factor a perfect square on the left side:
(r + 2.25)(r + 2.25) = -35.4375

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
r = {0}