(5y^2+7y-7)-(4y^2-6y+1)+(8y^2-6y+3)=

Solution for (5y^2+7y-7)-(4y^2-6y+1)+(8y^2-6y+3)= equation:

Simplifying
(5y2 + 7y + -7) + -1(4y2 + -6y + 1) + (8y2 + -6y + 3) = 0

Reorder the terms:
(-7 + 7y + 5y2) + -1(4y2 + -6y + 1) + (8y2 + -6y + 3) = 0

Remove parenthesis around (-7 + 7y + 5y2)
-7 + 7y + 5y2 + -1(4y2 + -6y + 1) + (8y2 + -6y + 3) = 0

Reorder the terms:
-7 + 7y + 5y2 + -1(1 + -6y + 4y2) + (8y2 + -6y + 3) = 0
-7 + 7y + 5y2 + (1 * -1 + -6y * -1 + 4y2 * -1) + (8y2 + -6y + 3) = 0
-7 + 7y + 5y2 + (-1 + 6y + -4y2) + (8y2 + -6y + 3) = 0

Reorder the terms:
-7 + 7y + 5y2 + -1 + 6y + -4y2 + (3 + -6y + 8y2) = 0

Remove parenthesis around (3 + -6y + 8y2)
-7 + 7y + 5y2 + -1 + 6y + -4y2 + 3 + -6y + 8y2 = 0

Reorder the terms:
-7 + -1 + 3 + 7y + 6y + -6y + 5y2 + -4y2 + 8y2 = 0

Combine like terms: -7 + -1 = -8
-8 + 3 + 7y + 6y + -6y + 5y2 + -4y2 + 8y2 = 0

Combine like terms: -8 + 3 = -5
-5 + 7y + 6y + -6y + 5y2 + -4y2 + 8y2 = 0

Combine like terms: 7y + 6y = 13y
-5 + 13y + -6y + 5y2 + -4y2 + 8y2 = 0

Combine like terms: 13y + -6y = 7y
-5 + 7y + 5y2 + -4y2 + 8y2 = 0

Combine like terms: 5y2 + -4y2 = 1y2
-5 + 7y + 1y2 + 8y2 = 0

Combine like terms: 1y2 + 8y2 = 9y2
-5 + 7y + 9y2 = 0

Solving
-5 + 7y + 9y2 = 0

Solving for variable 'y'.

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

Divide each side by '9'.
-0.5555555556 + 0.7777777778y + y2 = 0

Move the constant term to the right:

Add '0.5555555556' to each side of the equation.
-0.5555555556 + 0.7777777778y + 0.5555555556 + y2 = 0 + 0.5555555556

Reorder the terms:
-0.5555555556 + 0.5555555556 + 0.7777777778y + y2 = 0 + 0.5555555556

Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000
0.0000000000 + 0.7777777778y + y2 = 0 + 0.5555555556
0.7777777778y + y2 = 0 + 0.5555555556

Combine like terms: 0 + 0.5555555556 = 0.5555555556
0.7777777778y + y2 = 0.5555555556

The y term is 0.7777777778y.  Take half its coefficient (0.3888888889).
Square it (0.1512345679) and add it to both sides.

Add '0.1512345679' to each side of the equation.
0.7777777778y + 0.1512345679 + y2 = 0.5555555556 + 0.1512345679

Reorder the terms:
0.1512345679 + 0.7777777778y + y2 = 0.5555555556 + 0.1512345679

Combine like terms: 0.5555555556 + 0.1512345679 = 0.7067901235
0.1512345679 + 0.7777777778y + y2 = 0.7067901235

Factor a perfect square on the left side:
(y + 0.3888888889)(y + 0.3888888889) = 0.7067901235

Calculate the square root of the right side: 0.840708108

Break this problem into two subproblems by setting 
(y + 0.3888888889) equal to 0.840708108 and -0.840708108.

Subproblem 1
y + 0.3888888889 = 0.840708108

Simplifying
y + 0.3888888889 = 0.840708108

Reorder the terms:
0.3888888889 + y = 0.840708108

Solving
0.3888888889 + y = 0.840708108

Solving for variable 'y'.

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

Add '-0.3888888889' to each side of the equation.
0.3888888889 + -0.3888888889 + y = 0.840708108 + -0.3888888889

Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000
0.0000000000 + y = 0.840708108 + -0.3888888889
y = 0.840708108 + -0.3888888889

Combine like terms: 0.840708108 + -0.3888888889 = 0.4518192191
y = 0.4518192191

Simplifying
y = 0.4518192191

Subproblem 2
y + 0.3888888889 = -0.840708108

Simplifying
y + 0.3888888889 = -0.840708108

Reorder the terms:
0.3888888889 + y = -0.840708108

Solving
0.3888888889 + y = -0.840708108

Solving for variable 'y'.

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

Add '-0.3888888889' to each side of the equation.
0.3888888889 + -0.3888888889 + y = -0.840708108 + -0.3888888889

Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000
0.0000000000 + y = -0.840708108 + -0.3888888889
y = -0.840708108 + -0.3888888889

Combine like terms: -0.840708108 + -0.3888888889 = -1.2295969969
y = -1.2295969969

Simplifying
y = -1.2295969969

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.4518192191, -1.2295969969}