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

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

Simplifying
-1y(y2 + -7) + 4y2(2y + -5) = 0

Reorder the terms:
-1y(-7 + y2) + 4y2(2y + -5) = 0
(-7 * -1y + y2 * -1y) + 4y2(2y + -5) = 0
(7y + -1y3) + 4y2(2y + -5) = 0

Reorder the terms:
7y + -1y3 + 4y2(-5 + 2y) = 0
7y + -1y3 + (-5 * 4y2 + 2y * 4y2) = 0
7y + -1y3 + (-20y2 + 8y3) = 0

Reorder the terms:
7y + -20y2 + -1y3 + 8y3 = 0

Combine like terms: -1y3 + 8y3 = 7y3
7y + -20y2 + 7y3 = 0

Solving
7y + -20y2 + 7y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(7 + -20y + 7y2) = 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 '(7 + -20y + 7y2)' equal to zero and attempt to solve:

Simplifying
7 + -20y + 7y2 = 0

Solving
7 + -20y + 7y2 = 0

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

Divide each side by '7'.
1 + -2.857142857y + y2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2.857142857y + -1 + y2 = 0 + -1

Reorder the terms:
1 + -1 + -2.857142857y + y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2.857142857y + y2 = 0 + -1
-2.857142857y + y2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2.857142857y + y2 = -1

The y term is -2.857142857y.  Take half its coefficient (-1.428571429).
Square it (2.040816328) and add it to both sides.

Add '2.040816328' to each side of the equation.
-2.857142857y + 2.040816328 + y2 = -1 + 2.040816328

Reorder the terms:
2.040816328 + -2.857142857y + y2 = -1 + 2.040816328

Combine like terms: -1 + 2.040816328 = 1.040816328
2.040816328 + -2.857142857y + y2 = 1.040816328

Factor a perfect square on the left side:
(y + -1.428571429)(y + -1.428571429) = 1.040816328

Calculate the square root of the right side: 1.020204062

Break this problem into two subproblems by setting 
(y + -1.428571429) equal to 1.020204062 and -1.020204062.

Subproblem 1
y + -1.428571429 = 1.020204062

Simplifying
y + -1.428571429 = 1.020204062

Reorder the terms:
-1.428571429 + y = 1.020204062

Solving
-1.428571429 + y = 1.020204062

Solving for variable 'y'.

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

Add '1.428571429' to each side of the equation.
-1.428571429 + 1.428571429 + y = 1.020204062 + 1.428571429

Combine like terms: -1.428571429 + 1.428571429 = 0.000000000
0.000000000 + y = 1.020204062 + 1.428571429
y = 1.020204062 + 1.428571429

Combine like terms: 1.020204062 + 1.428571429 = 2.448775491
y = 2.448775491

Simplifying
y = 2.448775491

Subproblem 2
y + -1.428571429 = -1.020204062

Simplifying
y + -1.428571429 = -1.020204062

Reorder the terms:
-1.428571429 + y = -1.020204062

Solving
-1.428571429 + y = -1.020204062

Solving for variable 'y'.

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

Add '1.428571429' to each side of the equation.
-1.428571429 + 1.428571429 + y = -1.020204062 + 1.428571429

Combine like terms: -1.428571429 + 1.428571429 = 0.000000000
0.000000000 + y = -1.020204062 + 1.428571429
y = -1.020204062 + 1.428571429

Combine like terms: -1.020204062 + 1.428571429 = 0.408367367
y = 0.408367367

Simplifying
y = 0.408367367

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.448775491, 0.408367367}
Solution
y = {0, 2.448775491, 0.408367367}