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

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

Simplifying
(-4y2 + 4y + 5) + -1(3y2 + -7y + -2) + (-3y2 + 5y + 5) = 0

Reorder the terms:
(5 + 4y + -4y2) + -1(3y2 + -7y + -2) + (-3y2 + 5y + 5) = 0

Remove parenthesis around (5 + 4y + -4y2)
5 + 4y + -4y2 + -1(3y2 + -7y + -2) + (-3y2 + 5y + 5) = 0

Reorder the terms:
5 + 4y + -4y2 + -1(-2 + -7y + 3y2) + (-3y2 + 5y + 5) = 0
5 + 4y + -4y2 + (-2 * -1 + -7y * -1 + 3y2 * -1) + (-3y2 + 5y + 5) = 0
5 + 4y + -4y2 + (2 + 7y + -3y2) + (-3y2 + 5y + 5) = 0

Reorder the terms:
5 + 4y + -4y2 + 2 + 7y + -3y2 + (5 + 5y + -3y2) = 0

Remove parenthesis around (5 + 5y + -3y2)
5 + 4y + -4y2 + 2 + 7y + -3y2 + 5 + 5y + -3y2 = 0

Reorder the terms:
5 + 2 + 5 + 4y + 7y + 5y + -4y2 + -3y2 + -3y2 = 0

Combine like terms: 5 + 2 = 7
7 + 5 + 4y + 7y + 5y + -4y2 + -3y2 + -3y2 = 0

Combine like terms: 7 + 5 = 12
12 + 4y + 7y + 5y + -4y2 + -3y2 + -3y2 = 0

Combine like terms: 4y + 7y = 11y
12 + 11y + 5y + -4y2 + -3y2 + -3y2 = 0

Combine like terms: 11y + 5y = 16y
12 + 16y + -4y2 + -3y2 + -3y2 = 0

Combine like terms: -4y2 + -3y2 = -7y2
12 + 16y + -7y2 + -3y2 = 0

Combine like terms: -7y2 + -3y2 = -10y2
12 + 16y + -10y2 = 0

Solving
12 + 16y + -10y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 8y + -5y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + 8y + -5y2)' equal to zero and attempt to solve:

Simplifying
6 + 8y + -5y2 = 0

Solving
6 + 8y + -5y2 = 0

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

Divide each side by '-5'.
-1.2 + -1.6y + y2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + -1.6y + 1.2 + y2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + -1.6y + y2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + -1.6y + y2 = 0 + 1.2
-1.6y + y2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
-1.6y + y2 = 1.2

The y term is -1.6y.  Take half its coefficient (-0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
-1.6y + 0.64 + y2 = 1.2 + 0.64

Reorder the terms:
0.64 + -1.6y + y2 = 1.2 + 0.64

Combine like terms: 1.2 + 0.64 = 1.84
0.64 + -1.6y + y2 = 1.84

Factor a perfect square on the left side:
(y + -0.8)(y + -0.8) = 1.84

Calculate the square root of the right side: 1.356465997

Break this problem into two subproblems by setting 
(y + -0.8) equal to 1.356465997 and -1.356465997.

Subproblem 1
y + -0.8 = 1.356465997

Simplifying
y + -0.8 = 1.356465997

Reorder the terms:
-0.8 + y = 1.356465997

Solving
-0.8 + y = 1.356465997

Solving for variable 'y'.

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

Add '0.8' to each side of the equation.
-0.8 + 0.8 + y = 1.356465997 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + y = 1.356465997 + 0.8
y = 1.356465997 + 0.8

Combine like terms: 1.356465997 + 0.8 = 2.156465997
y = 2.156465997

Simplifying
y = 2.156465997

Subproblem 2
y + -0.8 = -1.356465997

Simplifying
y + -0.8 = -1.356465997

Reorder the terms:
-0.8 + y = -1.356465997

Solving
-0.8 + y = -1.356465997

Solving for variable 'y'.

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

Add '0.8' to each side of the equation.
-0.8 + 0.8 + y = -1.356465997 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + y = -1.356465997 + 0.8
y = -1.356465997 + 0.8

Combine like terms: -1.356465997 + 0.8 = -0.556465997
y = -0.556465997

Simplifying
y = -0.556465997

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.156465997, -0.556465997}
Solution
y = {2.156465997, -0.556465997}