10y^3+20y^2+55y=

Solution for 10y^3+20y^2+55y= equation:

Simplifying
10y3 + 20y2 + 55y = 0

Reorder the terms:
55y + 20y2 + 10y3 = 0

Solving
55y + 20y2 + 10y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5y'.
5y(11 + 4y + 2y2) = 0

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

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(11 + 4y + 2y2)' equal to zero and attempt to solve:

Simplifying
11 + 4y + 2y2 = 0

Solving
11 + 4y + 2y2 = 0

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

Divide each side by '2'.
5.5 + 2y + y2 = 0

Move the constant term to the right:

Add '-5.5' to each side of the equation.
5.5 + 2y + -5.5 + y2 = 0 + -5.5

Reorder the terms:
5.5 + -5.5 + 2y + y2 = 0 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + 2y + y2 = 0 + -5.5
2y + y2 = 0 + -5.5

Combine like terms: 0 + -5.5 = -5.5
2y + y2 = -5.5

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

Add '1' to each side of the equation.
2y + 1 + y2 = -5.5 + 1

Reorder the terms:
1 + 2y + y2 = -5.5 + 1

Combine like terms: -5.5 + 1 = -4.5
1 + 2y + y2 = -4.5

Factor a perfect square on the left side:
(y + 1)(y + 1) = -4.5

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
y = {0}