(4y^2-7y-1)-(-2y^2+7y+4)+(6y^2-9y-9)=0

Solution for (4y^2-7y-1)-(-2y^2+7y+4)+(6y^2-9y-9)=0 equation:

Simplifying
(4y2 + -7y + -1) + -1(-2y2 + 7y + 4) + (6y2 + -9y + -9) = 0

Reorder the terms:
(-1 + -7y + 4y2) + -1(-2y2 + 7y + 4) + (6y2 + -9y + -9) = 0

Remove parenthesis around (-1 + -7y + 4y2)
-1 + -7y + 4y2 + -1(-2y2 + 7y + 4) + (6y2 + -9y + -9) = 0

Reorder the terms:
-1 + -7y + 4y2 + -1(4 + 7y + -2y2) + (6y2 + -9y + -9) = 0
-1 + -7y + 4y2 + (4 * -1 + 7y * -1 + -2y2 * -1) + (6y2 + -9y + -9) = 0
-1 + -7y + 4y2 + (-4 + -7y + 2y2) + (6y2 + -9y + -9) = 0

Reorder the terms:
-1 + -7y + 4y2 + -4 + -7y + 2y2 + (-9 + -9y + 6y2) = 0

Remove parenthesis around (-9 + -9y + 6y2)
-1 + -7y + 4y2 + -4 + -7y + 2y2 + -9 + -9y + 6y2 = 0

Reorder the terms:
-1 + -4 + -9 + -7y + -7y + -9y + 4y2 + 2y2 + 6y2 = 0

Combine like terms: -1 + -4 = -5
-5 + -9 + -7y + -7y + -9y + 4y2 + 2y2 + 6y2 = 0

Combine like terms: -5 + -9 = -14
-14 + -7y + -7y + -9y + 4y2 + 2y2 + 6y2 = 0

Combine like terms: -7y + -7y = -14y
-14 + -14y + -9y + 4y2 + 2y2 + 6y2 = 0

Combine like terms: -14y + -9y = -23y
-14 + -23y + 4y2 + 2y2 + 6y2 = 0

Combine like terms: 4y2 + 2y2 = 6y2
-14 + -23y + 6y2 + 6y2 = 0

Combine like terms: 6y2 + 6y2 = 12y2
-14 + -23y + 12y2 = 0

Solving
-14 + -23y + 12y2 = 0

Solving for variable 'y'.

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

Divide each side by '12'.
-1.166666667 + -1.916666667y + y2 = 0

Move the constant term to the right:

Add '1.166666667' to each side of the equation.
-1.166666667 + -1.916666667y + 1.166666667 + y2 = 0 + 1.166666667

Reorder the terms:
-1.166666667 + 1.166666667 + -1.916666667y + y2 = 0 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + -1.916666667y + y2 = 0 + 1.166666667
-1.916666667y + y2 = 0 + 1.166666667

Combine like terms: 0 + 1.166666667 = 1.166666667
-1.916666667y + y2 = 1.166666667

The y term is -1.916666667y.  Take half its coefficient (-0.9583333335).
Square it (0.9184027781) and add it to both sides.

Add '0.9184027781' to each side of the equation.
-1.916666667y + 0.9184027781 + y2 = 1.166666667 + 0.9184027781

Reorder the terms:
0.9184027781 + -1.916666667y + y2 = 1.166666667 + 0.9184027781

Combine like terms: 1.166666667 + 0.9184027781 = 2.0850694451
0.9184027781 + -1.916666667y + y2 = 2.0850694451

Factor a perfect square on the left side:
(y + -0.9583333335)(y + -0.9583333335) = 2.0850694451

Calculate the square root of the right side: 1.443976954

Break this problem into two subproblems by setting 
(y + -0.9583333335) equal to 1.443976954 and -1.443976954.

Subproblem 1
y + -0.9583333335 = 1.443976954

Simplifying
y + -0.9583333335 = 1.443976954

Reorder the terms:
-0.9583333335 + y = 1.443976954

Solving
-0.9583333335 + y = 1.443976954

Solving for variable 'y'.

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

Add '0.9583333335' to each side of the equation.
-0.9583333335 + 0.9583333335 + y = 1.443976954 + 0.9583333335

Combine like terms: -0.9583333335 + 0.9583333335 = 0.0000000000
0.0000000000 + y = 1.443976954 + 0.9583333335
y = 1.443976954 + 0.9583333335

Combine like terms: 1.443976954 + 0.9583333335 = 2.4023102875
y = 2.4023102875

Simplifying
y = 2.4023102875

Subproblem 2
y + -0.9583333335 = -1.443976954

Simplifying
y + -0.9583333335 = -1.443976954

Reorder the terms:
-0.9583333335 + y = -1.443976954

Solving
-0.9583333335 + y = -1.443976954

Solving for variable 'y'.

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

Add '0.9583333335' to each side of the equation.
-0.9583333335 + 0.9583333335 + y = -1.443976954 + 0.9583333335

Combine like terms: -0.9583333335 + 0.9583333335 = 0.0000000000
0.0000000000 + y = -1.443976954 + 0.9583333335
y = -1.443976954 + 0.9583333335

Combine like terms: -1.443976954 + 0.9583333335 = -0.4856436205
y = -0.4856436205

Simplifying
y = -0.4856436205

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.4023102875, -0.4856436205}