(7y^3-3y)+(8y^2-8y)=

Solution for (7y^3-3y)+(8y^2-8y)= equation:

Simplifying
(7y3 + -3y) + (8y2 + -8y) = 0

Reorder the terms:
(-3y + 7y3) + (8y2 + -8y) = 0

Remove parenthesis around (-3y + 7y3)
-3y + 7y3 + (8y2 + -8y) = 0

Reorder the terms:
-3y + 7y3 + (-8y + 8y2) = 0

Remove parenthesis around (-8y + 8y2)
-3y + 7y3 + -8y + 8y2 = 0

Reorder the terms:
-3y + -8y + 8y2 + 7y3 = 0

Combine like terms: -3y + -8y = -11y
-11y + 8y2 + 7y3 = 0

Solving
-11y + 8y2 + 7y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-11 + 8y + 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 '(-11 + 8y + 7y2)' equal to zero and attempt to solve:

Simplifying
-11 + 8y + 7y2 = 0

Solving
-11 + 8y + 7y2 = 0

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

Divide each side by '7'.
-1.571428571 + 1.142857143y + y2 = 0

Move the constant term to the right:

Add '1.571428571' to each side of the equation.
-1.571428571 + 1.142857143y + 1.571428571 + y2 = 0 + 1.571428571

Reorder the terms:
-1.571428571 + 1.571428571 + 1.142857143y + y2 = 0 + 1.571428571

Combine like terms: -1.571428571 + 1.571428571 = 0.000000000
0.000000000 + 1.142857143y + y2 = 0 + 1.571428571
1.142857143y + y2 = 0 + 1.571428571

Combine like terms: 0 + 1.571428571 = 1.571428571
1.142857143y + y2 = 1.571428571

The y term is 1.142857143y.  Take half its coefficient (0.5714285715).
Square it (0.3265306123) and add it to both sides.

Add '0.3265306123' to each side of the equation.
1.142857143y + 0.3265306123 + y2 = 1.571428571 + 0.3265306123

Reorder the terms:
0.3265306123 + 1.142857143y + y2 = 1.571428571 + 0.3265306123

Combine like terms: 1.571428571 + 0.3265306123 = 1.8979591833
0.3265306123 + 1.142857143y + y2 = 1.8979591833

Factor a perfect square on the left side:
(y + 0.5714285715)(y + 0.5714285715) = 1.8979591833

Calculate the square root of the right side: 1.377664394

Break this problem into two subproblems by setting 
(y + 0.5714285715) equal to 1.377664394 and -1.377664394.

Subproblem 1
y + 0.5714285715 = 1.377664394

Simplifying
y + 0.5714285715 = 1.377664394

Reorder the terms:
0.5714285715 + y = 1.377664394

Solving
0.5714285715 + y = 1.377664394

Solving for variable 'y'.

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

Add '-0.5714285715' to each side of the equation.
0.5714285715 + -0.5714285715 + y = 1.377664394 + -0.5714285715

Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000
0.0000000000 + y = 1.377664394 + -0.5714285715
y = 1.377664394 + -0.5714285715

Combine like terms: 1.377664394 + -0.5714285715 = 0.8062358225
y = 0.8062358225

Simplifying
y = 0.8062358225

Subproblem 2
y + 0.5714285715 = -1.377664394

Simplifying
y + 0.5714285715 = -1.377664394

Reorder the terms:
0.5714285715 + y = -1.377664394

Solving
0.5714285715 + y = -1.377664394

Solving for variable 'y'.

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

Add '-0.5714285715' to each side of the equation.
0.5714285715 + -0.5714285715 + y = -1.377664394 + -0.5714285715

Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000
0.0000000000 + y = -1.377664394 + -0.5714285715
y = -1.377664394 + -0.5714285715

Combine like terms: -1.377664394 + -0.5714285715 = -1.9490929655
y = -1.9490929655

Simplifying
y = -1.9490929655

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.8062358225, -1.9490929655}
Solution
y = {0, 0.8062358225, -1.9490929655}