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

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

Simplifying
-1y5(7y2 + 4y + -7) = 0

Reorder the terms:
-1y5(-7 + 4y + 7y2) = 0
(-7 * -1y5 + 4y * -1y5 + 7y2 * -1y5) = 0
(7y5 + -4y6 + -7y7) = 0

Solving
7y5 + -4y6 + -7y7 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y5'.
y5(7 + -4y + -7y2) = 0

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 '(7 + -4y + -7y2)' equal to zero and attempt to solve:

Simplifying
7 + -4y + -7y2 = 0

Solving
7 + -4y + -7y2 = 0

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

Divide each side by '-7'.
-1 + 0.5714285714y + y2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.5714285714y + 1 + y2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.5714285714y + y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.5714285714y + y2 = 0 + 1
0.5714285714y + y2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.5714285714y + y2 = 1

The y term is 0.5714285714y.  Take half its coefficient (0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
0.5714285714y + 0.08163265305 + y2 = 1 + 0.08163265305

Reorder the terms:
0.08163265305 + 0.5714285714y + y2 = 1 + 0.08163265305

Combine like terms: 1 + 0.08163265305 = 1.08163265305
0.08163265305 + 0.5714285714y + y2 = 1.08163265305

Factor a perfect square on the left side:
(y + 0.2857142857)(y + 0.2857142857) = 1.08163265305

Calculate the square root of the right side: 1.040015698

Break this problem into two subproblems by setting 
(y + 0.2857142857) equal to 1.040015698 and -1.040015698.

Subproblem 1
y + 0.2857142857 = 1.040015698

Simplifying
y + 0.2857142857 = 1.040015698

Reorder the terms:
0.2857142857 + y = 1.040015698

Solving
0.2857142857 + y = 1.040015698

Solving for variable 'y'.

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

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -0.2857142857 + y = 1.040015698 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + y = 1.040015698 + -0.2857142857
y = 1.040015698 + -0.2857142857

Combine like terms: 1.040015698 + -0.2857142857 = 0.7543014123
y = 0.7543014123

Simplifying
y = 0.7543014123

Subproblem 2
y + 0.2857142857 = -1.040015698

Simplifying
y + 0.2857142857 = -1.040015698

Reorder the terms:
0.2857142857 + y = -1.040015698

Solving
0.2857142857 + y = -1.040015698

Solving for variable 'y'.

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

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -0.2857142857 + y = -1.040015698 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + y = -1.040015698 + -0.2857142857
y = -1.040015698 + -0.2857142857

Combine like terms: -1.040015698 + -0.2857142857 = -1.3257299837
y = -1.3257299837

Simplifying
y = -1.3257299837

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.7543014123, -1.3257299837}
Solution
y = {0.7543014123, -1.3257299837}