2y^3(5y^4-7y^3+y^2)=

Solution for 2y^3(5y^4-7y^3+y^2)= equation:

Simplifying
2y3(5y4 + -7y3 + y2) = 0

Reorder the terms:
2y3(y2 + -7y3 + 5y4) = 0
(y2 * 2y3 + -7y3 * 2y3 + 5y4 * 2y3) = 0
(2y5 + -14y6 + 10y7) = 0

Solving
2y5 + -14y6 + 10y7 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2y5'.
2y5(1 + -7y + 5y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'y5' equal to zero and attempt to solve:

Simplifying
y5 = 0

Solving
y5 = 0

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

Simplifying
y5 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(1 + -7y + 5y2)' equal to zero and attempt to solve:

Simplifying
1 + -7y + 5y2 = 0

Solving
1 + -7y + 5y2 = 0

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

Divide each side by '5'.
0.2 + -1.4y + y2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -1.4y + -0.2 + y2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -1.4y + y2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -1.4y + y2 = 0 + -0.2
-1.4y + y2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-1.4y + y2 = -0.2

The y term is -1.4y.  Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
-1.4y + 0.49 + y2 = -0.2 + 0.49

Reorder the terms:
0.49 + -1.4y + y2 = -0.2 + 0.49

Combine like terms: -0.2 + 0.49 = 0.29
0.49 + -1.4y + y2 = 0.29

Factor a perfect square on the left side:
(y + -0.7)(y + -0.7) = 0.29

Calculate the square root of the right side: 0.538516481

Break this problem into two subproblems by setting 
(y + -0.7) equal to 0.538516481 and -0.538516481.

Subproblem 1
y + -0.7 = 0.538516481

Simplifying
y + -0.7 = 0.538516481

Reorder the terms:
-0.7 + y = 0.538516481

Solving
-0.7 + y = 0.538516481

Solving for variable 'y'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + y = 0.538516481 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + y = 0.538516481 + 0.7
y = 0.538516481 + 0.7

Combine like terms: 0.538516481 + 0.7 = 1.238516481
y = 1.238516481

Simplifying
y = 1.238516481

Subproblem 2
y + -0.7 = -0.538516481

Simplifying
y + -0.7 = -0.538516481

Reorder the terms:
-0.7 + y = -0.538516481

Solving
-0.7 + y = -0.538516481

Solving for variable 'y'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + y = -0.538516481 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + y = -0.538516481 + 0.7
y = -0.538516481 + 0.7

Combine like terms: -0.538516481 + 0.7 = 0.161483519
y = 0.161483519

Simplifying
y = 0.161483519

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.238516481, 0.161483519}
Solution
y = {1.238516481, 0.161483519}