14y^3-28y^2+y=

Solution for 14y^3-28y^2+y= equation:

Simplifying
14y3 + -28y2 + y = 0

Reorder the terms:
y + -28y2 + 14y3 = 0

Solving
y + -28y2 + 14y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(1 + -28y + 14y2) = 0

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 '(1 + -28y + 14y2)' equal to zero and attempt to solve:

Simplifying
1 + -28y + 14y2 = 0

Solving
1 + -28y + 14y2 = 0

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

Divide each side by '14'.
0.07142857143 + -2y + y2 = 0

Move the constant term to the right:

Add '-0.07142857143' to each side of the equation.
0.07142857143 + -2y + -0.07142857143 + y2 = 0 + -0.07142857143

Reorder the terms:
0.07142857143 + -0.07142857143 + -2y + y2 = 0 + -0.07142857143

Combine like terms: 0.07142857143 + -0.07142857143 = 0.00000000000
0.00000000000 + -2y + y2 = 0 + -0.07142857143
-2y + y2 = 0 + -0.07142857143

Combine like terms: 0 + -0.07142857143 = -0.07142857143
-2y + y2 = -0.07142857143

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 = -0.07142857143 + 1

Reorder the terms:
1 + -2y + y2 = -0.07142857143 + 1

Combine like terms: -0.07142857143 + 1 = 0.92857142857
1 + -2y + y2 = 0.92857142857

Factor a perfect square on the left side:
(y + -1)(y + -1) = 0.92857142857

Calculate the square root of the right side: 0.963624112

Break this problem into two subproblems by setting 
(y + -1) equal to 0.963624112 and -0.963624112.

Subproblem 1
y + -1 = 0.963624112

Simplifying
y + -1 = 0.963624112

Reorder the terms:
-1 + y = 0.963624112

Solving
-1 + y = 0.963624112

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = 0.963624112 + 1

Combine like terms: -1 + 1 = 0
0 + y = 0.963624112 + 1
y = 0.963624112 + 1

Combine like terms: 0.963624112 + 1 = 1.963624112
y = 1.963624112

Simplifying
y = 1.963624112

Subproblem 2
y + -1 = -0.963624112

Simplifying
y + -1 = -0.963624112

Reorder the terms:
-1 + y = -0.963624112

Solving
-1 + y = -0.963624112

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = -0.963624112 + 1

Combine like terms: -1 + 1 = 0
0 + y = -0.963624112 + 1
y = -0.963624112 + 1

Combine like terms: -0.963624112 + 1 = 0.036375888
y = 0.036375888

Simplifying
y = 0.036375888

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.963624112, 0.036375888}
Solution
y = {0, 1.963624112, 0.036375888}